Which Ante-Nicene Church Fathers believed that Jesus is the "eternal Son" of the Father? Economic trinitarianism, in the pre-Nicene sense of the phrase, says that God is a monad who becomes tripartite for the purposes of creation and redemption. Forms of this view were held by Justin Martyr and Tertullian, but were rejected at Nicaea in favor of the orthodox teaching of an eternal Trinity, in which the Son is eternal (The Eternal Generation of the Son: Maintaining Orthodoxy in Trinitarian Theology, Page 97).

Who among the ante-Nicene church fathers opposed economic trinitarianism and believed that Jesus is the "eternal Son" of the Father?
The following Ante-Nicene church fathers believed in Jesus as the eternal Son:

2nd century

Irenaeus (AD. 120-200) said: 


  "But the Son, eternally co-existing with the Father, from of old, yea,
  from the beginning, always reveals the Father to Angels, Archangels,
  Powers, Virtues..." (Against Heresies, Book II, ch. 30, section 9)


Athenagoras ( A.D. 177) said:


  “We acknowledge one God, uncreated, eternal, invisible, impassable
  [i.e., not subject to suffering], incomprehensible, illimitable … by
  whom the universe has been created through his Logos … We acknowledge
  also a Son of God. Nor let anyone think it ridiculous that God should
  have a Son … the Son of God is the Logos of the Father. If … it occurs
  to you to inquire what is meant by the Son, I will state briefly that
  he is the first product of the Father, not as having been brought
  into existence, for from the beginning God, who is the eternal mind,
  had theLogos in himself, being from eternity instinct with Logos.
  (Plea for the Christians ch. 10)


Clement of Alexnadria ( AD. 150-215) said: 


  When [John] says, "from the beginning," the elder explained to this
  effect, that the beginning of generation is not separated from the
  beginning of the Creator. For when he says, "That which is from the
  beginning," he touches on the generation without beginning of the Son,
  who is co-existent with the Father. There was, then, a Word importing
  an unbeginning eternity, as also the Word itself, that is, the Son
  of God, who being by equality of substance one with the Father, is
  eternal and uncreated.(Fragments of Clement of Alexandria: Comments
  on the First Epistle of John from The Ante-Nicene Fathers, vol. II)


3rd century

Gregory Thaumaturgus (A.D. 213-270) said:


  There is one God, the Father of the living Word, who is His subsistent
  Wisdom and Power and Eternal Image:perfect Begetter of the perfect
  Begotten, Father of the only-begotten Son. There is one Lord, Only of
  the Only,God of God, Image and Likeness of Deity, Efficient Word,
  Wisdom comprehensive of the constitution of all things, and Power
  formative of the whole creation, true Son of true Father, Invisible of
  Invisible, and Incorruptible of Incorruptible,and Immortal of Immortal
  and Eternal of Eternal. And there is One Holy Spirit, having His
  subsistence from God, and being made manifest by the Son, to wit to
  men: Image of the Son, Perfect Image of the Perfect; Life, the Cause
  of the living; Holy Fount; Sanctity, the Supplier, or Leader, of
  Sanctification; in whom is manifested God the Father, who is above all
  and in all, and God the Son, who is through all. There is a perfect
  Trinity, in glory and eternity and sovereignty, neither divided nor
  estranged. Wherefore there is nothing either created or in servitude
  in the Trinity; nor anything superinduced, as if at some former period
  it was non-existent, and at some later period it was introduced. And
  thus neither was the Son ever wanting to the Father, nor the Spirit to
  the Son; but without variation and without change, the same Trinity
  abides ever.


Novatian (A.D. 200- 258) said:


  To the Son alone they are known, who has known the secrets of the
  Father. He then, since He was begotten of the Father, is always in
  the Father. And I thus say always, that I may show Him not to be
  unborn, but born. But He who is before all time must be said to have
  been always in the Father; for no time can be assigned to Him who is
  before all time (On the Trinity, 31.3).


Dionysius of Rome (A.D. ? - 268) said:


  "A blasphemy then is it, not ordinary, but even the highest, to say that the Lord is in any sort a handiwork. For if He came to be Son,
  once He was not; but He was always, if (that is) He be in the Father,
  as He says Himself, and if the Christ be Word and Wisdom and Power
  (which, as ye know, divine Scripture says), and these attributes be
  powers of God. If then the Son came into being, once these attributes
  were not; consequently there was a time, when God was without them;
  which is most absurd. And why say more on these points to you, men
  full of the Spirit and well aware of the absurdities which come to
  view from saying that the Son is a work? Not attending, as I consider,
  to this circumstance, the authors of this opinion have entirely missed
  the truth, in explaining, contrary to the sense of divine and
  prophetic Scripture in the passage, the words, ‘The Lord created me a
  beginning of His ways unto His works.’ For the sense of ‘He created,’
  as ye know, is not one, for we must understand ‘He created’ in this
  place, as ‘He set over the works made by Him,’ that is, ‘made by the
  Son Himself.’ And ‘He created’ here must not be taken for ‘made,’ for
  creating differs from making. ‘Is not He thy Father that hath bought
  thee? hath He not made thee and created thee?’ says Moses in his great
  song in Deuteronomy. And one may say to them, O reckless men, is He a
  work, who is ‘the First-born of every creature, who is born from the
  womb before the morning star,’ who said, as Wisdom, ‘Before all the
  hills He begets me?’ And in many passages of the divine oracles is the
  Son said to have been generated, but nowhere to have come into being;
  which manifestly convicts those of misconception about the Lord’s
  generation, who presume to call His divine and ineffable generation a
  making.Neither then may we divide into three Godheads the wonderful
  and divine Monad; nor disparage with the name of ‘work’ the dignity
  and exceeding majesty of the Lord; but we must believe in God the
  Father Almighty, and in Christ Jesus His Son, and in the Holy Ghost,
  and hold that to the God of the universe the Word is united. For ‘I,’
  says He, ‘and the Father are one;’ and, ‘I in the Father and the
  Father in Me.’ For thus both the Divine Triad, and the holy preaching
  of the Monarchy, will be preserved.” (Against Sabellians).