Historical Apologetic used by 7th Century Christians towards Early Muslims Regarding the Hypostatic Union and Jesus' Title "Son of God" According to my research Jesus is called the Son of God about 40 times in the NT. When interacting with Muslims, a common objection they give against Christ's deity, and the Trinity is that the Quran says God does not have a son.


  O FOLLOWERS of the Gospel! Do not overstep the bounds [of truth] in your religious beliefs, and do not say of God anything but the truth. The Christ Jesus, son of Mary, was but God's Apostle - [the fulfilment of] His promise which He had conveyed unto Mary - and a soul created by Him. Believe, then, in God and His apostles, and do not say, "[God is] a trinity". Desist [from this assertion] for your own good. God is but One God; utterly remote is He, in His glory, from having a son: unto Him belongs all that is in the heavens and all that is on earth; and none is as worthy of trust as God. - 4:171


Obviously Christian's have never historically taught that Jesus is the physical progeny of the Father and Mary. However, this is the first reaction I have always gotten when discussing Jesus' nature with Muslims. Is there any way to get some idea what the apologetic Christians interacting with early Muslims were using? I understand that the term "early Muslims" may not be entirely accurate since Mohammed had not amassed a large following when engaging with Christians and Jews in the area, but for now I think it's alright to use that label.

Please add other appropriate tags if you think of them.
James White discusses this in What Every Christian Needs to Know About the Qur'an. Here is the relevant quote with some emphasis added:


  One early source, the Tanwīr al-Miqbās min Tafsīr Ibn ’Abbās, directly connects the encounter with the Najran Christians with the text of Surah 4:
  
  
    Allah then revealed about the Nestorian Christians of Najran who claimed that Jesus was the son of Allah and that Jesus and the Lord are partners, saying: (O People of the Scripture! Do not exaggerate) do not be extreme (in your religion) for this is not the right course (nor utter aught concerning Allah save the Truth. The Messiah, Jesus son of Mary, was only a messenger of Allah, and His word which He conveyed unto Mary) and through His word he became a created being, (and a spirit from Him) and through His command, Jesus became a son without a father. (So believe in Allah and His messengers) all the messengers including Jesus, (and say not “Three”) a son, father and wife. (Cease!) from making such a claim and repent ((it is) better for you!) than such a claim. (Allah is only One God) without a son or partner. (Far is it removed from His Transcendent Majesty that he should have a son. His is all that is in the heavens and all that is in the earth) are His servants. (And Allah is sufficient as Defender) as Lord of all created beings and He is witness of what He says about Jesus.
  
  
  Chapter 4


(A complete copy of this Muslim source is available here).

This Muslim source claims that Jesus is not the progeny of God the Father and Mary -- which Christians would agree with -- and that it is an error to say that God is the Trinity ("Three") composed of the Father, the Son (Jesus), and the wife (Mary) -- which is a misstatement of the Christian doctrine of the Trinity (this is part of an argument by White that the Qur'an is ignorant of the Christian understanding of the Trinitarian God and that therefore the Qur'an is not divinely inspired). A similar argument using the same Muslim source can be found online here.

The other interesting information from this Muslim source is that the Christian teachings were given to the Muslims by Najran Christians who adhered to Nestorianism. Since Nestorianism is heterodox and claims that Jesus has separate divine and human natures it's possible that the Muslims understood the Nestorian Christians as claiming that Jesus' human nature was the progeny of God the Father and Mary.

White mentions the Najran Christians a bit later in his book, too (emphasis added):


  The earliest biography of Muhammad’s life, of Ibn Ishaq, contains a passage that not only demonstrates how primitive is this understanding of the Qur’anic teaching of “three” but also makes an astounding claim. Referring back to the deputation from Najran, we read,
  
  
    They were Christians according to the Byzantine rite, though they differed among themselves in some points, saying He is God; and He is the son of God; and He is the third person of the Trinity, which is the doctrine of Christianity. They argue that he is God because he used to raise the dead, and heal the sick, and declare the unseen; and make clay birds and then breathe into them so that they flew away; and all this was by the command of God Almighty, “We will make him a sign to men.” They argue that he is the son of God in that they say he had no known father; and he spoke in the cradle and this is something that no child of Adam has ever done. They argue that he is the third of three in that God says: We have done, We have commanded, We have created and We have decreed, and they say, If He were one he would have said I have done, I have created, and so on, but He is He and Jesus and Mary. Concerning all these assertions the Quran came down.
  
  
  Ibn Ishaq records that Christians believe the Trinity is “He and Jesus and Mary,” as do numerous other sources...
  
  Chapter 4


From this Muslim source it sounds like the Christians were not in agreement regarding the nature of Jesus and the Trinity, and that the Muslims understood them as claiming that Jesus was the third person of the Trinity (with the Father and Mary as the other two).

White mentions in the footnotes that the Muslim encounter with the Najran Christians is traditionally dated to be AD 632.