In Christian dogma, can Satan and the fallen angels (his demons) get married and have progeny? All of us know that Satan and his demons (fallen angels) have a role in temptation of Adam and his progeny. The question is can Satan and his demons get marry and have progeny? In Islam, Satan (Iblis) has progeny as mentioned in Quran. If Satan can get marry and has progeny, so why not unfallen angels can get marry and have  progeny?.
In Christian dogma, can Satan and the fallen angels (his demons) get married and have progeny?

According to Catholic theology: no.

The Catechism of the Catholic Church says the following about angels, both good and evil angels,in a general manner:


  The Angels
  
  The existence of angels - a truth of faith
  
  328 The existence of the spiritual, non-corporeal beings that Sacred Scripture usually calls "angels" is a truth of faith. The witness of Scripture is as clear as the unanimity of Tradition.
  
  Who are they?
  
  329 St. Augustine says: "'Angel' is the name of their office, not of their nature. If you seek the name of their nature, it is 'spirit'; if you seek the name of their office, it is 'angel': from what they are, 'spirit', from what they do, 'angel.'"188 With their whole beings the angels are servants and messengers of God. Because they "always behold the face of my Father who is in heaven" they are the "mighty ones who do his word, hearkening to the voice of his word".189
  
  330 **As purely spiritual creatures angels have intelligence and will: they are personal and immortal creatures, surpassing in perfection all visible creatures, as the splendor of their glory bears witness.**190


Only God can create life! God created them as angels before their fall. As spiritual beings they can not marry or have progeny either amongst themselves or with man. Only God created the angels in a state of angelic goodness. Just because some fell due to their angelic sin does not change anything

According to Catholic theology, the Devil and all the other evil demons are pure Spirits and as such can not alter their spiritual substance in order to become a physical or corporal being.

First of all, let us see how the Church defines a few terms.


  Demon
  
  Originally a spirit between the gods and men. In the New Testament a demon is the same as an evil spirit, which may be translated as "devil." It consequently means a malevolent, invisible being, which the pre-Christian word "demon" did not imply.
  
  Devil
  
  A fallen angel or evil spirit, especially the chief of the rebellious angels, Lucifer or Satan (Matthew 25). Adorned at his creation with sanctifying grace, he sinned by pride and along with many other angelic beings was denied the beatific vision. His abode is hell and he does not enjoy the benefits of Christ's redemption. Yet the devil remains a rational spirit, confirmed in evil, who is allowed by God to exercise some influence on living and inanimate creatures. 
  
  Man
  
  Latin homo, a human being, as distinct from vir, a male person. The term homo has no perfect English equivalent, but it is part of the Church's official vocabulary and occurs in every major document of the Catholic Church. A living substance, composed of a material body that dies and a spiritual soul that is immortal. Creature made by God to his image and likeness, to praise, reverence, and serve him in this life and thereby attain the eternal possession of God in the life to come. In philosophical terms, "man" is a rational animal, and collectively is the human species or the human race. 


Now Satan and all the other devils or demons are spiritual being composed of spiritual matter. They are pure spirit! Man is composed of a body and an immortal souls. Thus man in the fullest sense is both physical and spiritual in his essence; the demons are not!

According to the Church the evil spirits can not change their substance. They are spiritual beings and spiritual beings they shall remain.

Here is how St. Thomas Aquinas explains it:


  Some assert that the angels are composed of matter and form; which opinion Avicebron endeavored to establish in his book of the Fount of Life. For he supposes that whatever things are distinguished by the intellect are really distinct. Now as regards incorporeal substance, the intellect apprehends that which distinguishes it from corporeal substance, and that which it has in common with it. Hence he concludes that what distinguishes incorporeal from corporeal substance is a kind of form to it, and whatever is subject to this distinguishing form, as it were something common, is its matter. Therefore, he asserts the universal matter of spiritual and corporeal things is the same; so that it must be understood that the form of incorporeal substance is impressed in the matter of spiritual things, in the same way as the form of quantity is impressed in the matter of corporeal things.
  
  But one glance is enough to show that there cannot be one matter of spiritual and of corporeal things. For it is not possible that a spiritual and a corporeal form should be received into the same part of matter, otherwise one and the same thing would be corporeal and spiritual. Hence it would follow that one part of matter receives the corporeal form, and another receives the spiritual form. Matter, however, is not divisible into parts except as regarded under quantity; and without quantity substance is indivisible, as Aristotle says (Phys. i, text 15). Therefore it would follow that the matter of spiritual things is subject to quantity; which cannot be. Therefore it is impossible that corporeal and spiritual things should have the same matter.
  
  It is, further, impossible for an intellectual substance to have any kind of matter. For the operation belonging to anything is according to the mode of its substance. Now to understand is an altogether immaterial operation, as appears from its object, whence any act receives its species and nature. For a thing is understood according to its degree of immateriality; because forms that exist in matter are individual forms which the intellect cannot apprehend as such. Hence it must be that every intellectual substance is altogether immaterial.
  
  But things distinguished by the intellect are not necessarily distinguished in reality; because the intellect does not apprehend things according to their mode, but according to its own mode. Hence material things which are below our intellect exist in our intellect in a simpler mode than they exist in themselves. Angelic substances, on the other hand, are above our intellect; and hence our intellect cannot attain to apprehend them, as they are in themselves, but by its own mode, according as it apprehends composite things; and in this way also it apprehends God (Article 3).


Let us also look into who the Nephilim of the Scripture may truly be:


  The Nephilim (Hebrew: נְפִילִים) were the offspring of the "sons of God" and the "daughters of men" before the Deluge, according to Genesis 6:1-4. 
  
  A similar or identical biblical Hebrew term, read as "Nephilim" by some scholars, or as the word "fallen" by others, appears in Ezekiel 32:27.1 
  
  When people began to multiply on the face of the ground, and daughters were born to them, the sons of God saw that they were fair; and they took wives for themselves of all that they chose. Then the Lord said, "My spirit shall not abide in mortals forever, for they are flesh; their days shall be one hundred twenty years." The Nephilim were on the earth in those days—and also afterward—when the sons of God went in to the daughters of humans, who bore children to them. These were the heroes that were of old, warriors of renown. — Genesis 6:1–4, New Revised Standard Version
  
  The word is loosely translated as giants in some Bibles and left untranslated in others. The "sons of God" have been interpreted as fallen angels in some traditional Jewish explanations. 
  
  According to Numbers 13:33, they later inhabited Canaan at the time of the Israelite conquest of Canaan. 
  
  The Lord said to Moses, "Send men to spy out the land of Canaan, which I am giving to the Israelites" ... So they went up and spied out the land ... And they told him: "... Yet the people who live in the land are strong, and the towns are fortified and very large; and besides, we saw the descendants of Anak there." ... So they brought to the Israelites an unfavorable report of the land that they had spied out, saying, "The land that we have gone through as spies is a land that devours its inhabitants; and all the people that we saw in it are of great size. There we saw the Nephilim (the Anakites come from the Nephilim); and to ourselves we seemed like grasshoppers, and so we seemed to them." — Numbers 13:1–2; 21; 27–28; 32–33. New Revised Standard Version.


And now let us look at what the Sons of God may mean:


  Sons of the God (Hebrew: בני האלהים‎) literally: "sons of the Gods") is a phrase used in the Hebrew Bible and apocrypha. The phrase is also used in Kabbalah where bene elohim are part of different Jewish angelic hierarchies. 
  
  Hebrew Bible
  
  Genesis 6
  
  And it came to pass, when men began to multiply on the face of the earth, and daughters were born unto them, That the sons of God saw the daughters of men that they were fair; and they took them wives of all which they chose. And the LORD said, My spirit shall not always strive with man, for that he also is flesh: yet his days shall be an hundred and twenty years. There were giants in the earth in those days; and also after that, when the sons of God came in unto the daughters of men, and they bare children to them, the same became mighty men which were of old, men of renown. — Genesis 6:1–4, KJV
  
  The first mention of "sons of God" in the Hebrew Bible occurs at Genesis 6:1–4. In terms of literary-historical origin, this phrase is typically associated with the Jahwist tradition.4 
  
  This passage has had two interpretations in Judaism:
  
  
  Offspring of Seth: The first references to the offspring of Seth rebelling from God and mingling with the daughters of Cain are found in Christian and rabbinic literature from the second century CE onwards e.g. Rabbi Shimon bar Yochai, Augustine of Hippo, Julius Africanus, and the Letters attributed to St. Clement. It is also the view expressed in the modern canonical Amharic Ethiopian Orthodox Bible. In Judaism "Sons of God" usually refers to the righteous, i.e. the children of Seth.
  Angels: All of the earliest sources interpret the "sons of God" as angels. From the third century BCE onwards, references are found in the Enochic literature, the Dead Sea Scrolls the (Genesis Apocryphon, the Damascus Document, 4Q180), Jubilees, the Testament of Reuben, 2 Baruch, Josephus, and the book of Jude (compare with 2 Peter 2). This is also the meaning of the only two identical occurrences of bene ha elohim in the Hebrew Bible (Job 1:6 and 2:1), and of the most closely related expressions (refer to the list above). In the Septuagint, the interpretive reading "angels" is found in Codex Alexandrinus, one of four main witnesses to the Greek text.
  
  
  Rabbinic Judaism traditionally adheres to the first interpretation, with some exceptions, and modern Jewish translations may translate bnei elohim as "sons of rulers" rather than "sons of God". Regardless, the second interpretation (sons of angels or other divine beings) is nonexistent in modern Judaism. This is reflected by the rejection of Enoch and other Apocrypha supporting the second interpretation from the Hebrew Bible Canon. 


Using Scripture to interpret Scripture is a very common practice in our day and as such the New Testament in the person of St. Luke shows us that the Sons of God were the descendants of Adam.

According to Scripture “sons of God” means “persons who are begotten independently of any creature’s decision”. All angels can appropriately be called “sons of God”, but not all characters called “sons of God” in the Bible can appropriately be considered angels. The “sons of God” in Genesis 6:1-4 are undoubtedly human, and it is fitting to consider that they were created directly by God through transformation of human-like animals into persons.


  Who was the son of Enos, who was the son of Seth, who was the son of Adam, who was the son of God. - Luke 3:38