The text of the list itself is traditionally dated to about 170 because its author refers to Pius I, bishop of Rome (142 - 157), as recent:

But Hermas wrote The Shepherd very recently, in our times, in the city of Rome, while bishop Pius, his brother, was occupying the chair of the church of the city of Rome. And therefore it ought indeed to be read; but it cannot be read publicly to the people in church either among the Prophets, whose number is complete, or among the Apostles, for it is after their time. The assertions that the number of the Prophets is complete, and that the Apostles belong to an earlier time are a reaction to the mid second century charismatic movement called Montanism, which offered ongoing revelation.

The unidentified author accepts four Gospels, the last two of which are Luke and John, but the names of the first two are lost in the lacking beginning. Also accepted by the author are the "Acts of all Apostles" and 13 of the Pauline Epistles (but not the anonymous Epistle to the Hebrews, 1 and 2 Peter or, James). The author considers spurious the letters claiming to have Paul as author, and that claim to be written to the Laodiceans and to the Alexandrians, specifically said to be: "forged in Paul's name to [further] the heresy of Marcion."

Of the Catholic Epistles, the author accepts the Epistle of Jude and says that two epistles bearing the name of John are counted in the catholic Church; and the Book of Wisdom, "written by the friends of Solomon in his honour." The two epistles of John however are not identified further by the author, and there is no reason to assume that the John of the first letter is the same as that of the second - the church even officially regarded the canonical epistles of John as being by two different authors (whom they named John the Evangelist and John the Presbyter, respectively). The Apocalypse of Peter is mentioned as a book which some of us will not allow to be read in church, though it isn't certain whether this refers to the Greek Apocalypse of Peter or the quite different Coptic Apocalypse of Peter, the latter of which, unlike the former, was gnostic.

Translation

. . . at which nevertheless he was present, and so he placed [them in his narrative]. (2) The third book of the Gospel is that according to Luke. (3) Luke, the well-known physician, after the ascension of Christ, (4-5) when Paul had taken with him as one zealous for the law, (6) composed it in his own name, according to [the general] belief. Yet he himself had not (7) seen the Lord in the flesh; and therefore, as he was able to ascertain events, (8) so indeed he begins to tell the story from the birth of John. (9) The fourth of the Gospels is that of John, [one] of the disciples. (10) To his fellow disciples and bishops, who had been urging him [to write], (11) he said, 'Fast with me from today to three days, and what (12) will be revealed to each one (13) let us tell it to one another.' In the same night it was revealed (14) to Andrew, [one] of the apostles, (15-16) that John should write down all things in his own name while all of them should review it. And so, though various (17) elements may be taught in the individual books of the Gospels, (18) nevertheless this makes no difference to the faith of believers, since by the one sovereign Spirit all things (20) have been declared in all [the Gospels]: concerning the (21) nativity, concerning the passion, concerning the resurrection, (22) concerning life with his disciples, (23) and concerning his twofold coming; (24) the first in lowliness when he was despised, which has taken place, (25) the second glorious in royal power, (26) which is still in the future. What (27) marvel is it then, if John so consistently (28) mentions these particular points also in his Epistles, (29) saying about himself, 'What we have seen with our eyes (30) and heard with our ears and our hands (31) have handled, these things we have written to you? (32) For in this way he professes [himself] to be not only an eye-witness and hearer, (33) but also a writer of all the marvelous deeds of the Lord, in their order. (34) Moreover, the acts of all the apostles (35) were written in one book. For 'most excellent Theophilus' Luke compiled (36) the individual events that took place in his presence — (37) as he plainly shows by omitting the martyrdom of Peter (38) as well as the departure of Paul from the city [of Rome] (39) when he journeyed to Spain. As for the Epistles of (40-1) Paul, they themselves make clear to those desiring to understand, which ones [they are], from what place, or for what reason they were sent. (42) First of all, to the Corinthians, prohibiting their heretical schisms; (43) next, to the Galatians, against circumcision; (44-6) then to the Romans he wrote at length, explaining the order (or, plan) of the Scriptures, and also that Christ is their principle (or, main theme). It is necessary (47) for us to discuss these one by one, since the blessed (48) apostle Paul himself, following the example of his predecessor (49-50) John, writes by name to only seven churches in the following sequence: To the Corinthians (51) first, to the Ephesians second, to the Philippians third, (52) to the Colossians fourth, to the Galatians fifth, (53) to the Thessalonians sixth, to the Romans (54-5) seventh. It is true that he writes once more to the Corinthians and to the Thessalonians for the sake of admonition, (56-7) yet it is clearly recognizable that there is one Church spread throughout the whole extent of the earth. For John also in the (58) Apocalypse, though he writes to seven churches, (59-60) nevertheless speaks to all. [Paul also wrote] out of affection and love one to Philemon, one to Titus, and two to Timothy; and these are held sacred (62-3) in the esteem of the Church catholic for the regulation of ecclesiastical discipline. There is current also [an epistle] to (64) the Laodiceans, [and] another to the Alexandrians, [both] forged in Paul's (65) name to [further] the heresy of Marcion, and several others (66) which cannot be received into the catholic Church (67)— for it is not fitting that gall be mixed with honey. (68) Moreover, the epistle of Jude and two of the above-mentioned (or, bearing the name of) John are counted (or, used) in the catholic [Church]; and [the book of] Wisdom, (70) written by the friends of Solomon in his honour. (71) We receive only the apocalypses of John and Peter, (72) though some of us are not willing that the latter be read in church. (73) But Hermas wrote the Shepherd (74) very recently, in our times, in the city of Rome, (75) while bishop Pius, his brother, was occupying the [episcopal] chair (76) of the church of the city of Rome. (77) And therefore it ought indeed to be read; but (78) it cannot be read publicly to the people in church either among (79) the Prophets, whose number is complete, or among (80) the Apostles, for it is after [their] time. (81) But we accept nothing whatever of Arsinous or Valentinus or Miltiades, (82) who also composed (83) a new book of psalms for Marcion, (84-5) together with Basilides, the Asian founder of the Cataphrygians
  extracted from: http://www.bible-researcher.com/muratorian.html

Notes