No book of the New Testament includes a date when it was written. Moreover, folks living in that age didn’t even count time the way we do (i.e. BC-AD). Nevertheless, all New Testament books are deemed to have been written in the 1st Century, or, at the latest, shortly thereafter.
(All the authors and books listed here can be found in Annotated Bibliography on New Testament Text and Canon.)
Goodspeed, Edgar J. The Formation of the New Testament. University of Chicago Press, 1926, 210 pages.
“The books of the New Testament were written by various hands, at various places in the Greek world, and at various times between 50 and 150 A.D.” (p.1)
Smith, James E. Which Books Belong in the Bible? Lulu, 2009, p. 322-324.
Smith provides dates for each book, beginning with James in 48 A.D. and ending with the writings of John in 90 A. D.
Robinson, John A. T. Redating the New Testament. SCM Press, 1976, 370 pages.
Robinson dates the writing of the books between 40 and 70 AD, based primarily on the fact that none of the books make reference to the destruction of Jerusalem and its temple as having occurred. He lists specific dates for each book on page 352.
ESTIMATED DATES FOR INDIVIDUAL BOOKS
[Editorial note: The information here is incomplete; I will be adding to it over time. Note also that some of the sources in the section above provide specific dates for each book which may or may not be provided below. ]
Luke – would have been written before Acts
Acts -63 (per Stanley Porter)
Michael J. Kruger (in his “The Canonization of the New Testament” lectures found in iTunes U) says that the 27 New Testament documents are the only extant Christian writings from the 1st Century, with the possible exception of 1 Clement (95? 98?).
F. F. Bruce reports in a footnote on page 15 of The New Testament Documents: Are They Reliable? that J. A. T. Robinson argues in Redating the New Testament (1976) that everything in the New Testament was written before 70 AD.
“As stated by Nelson Glueck, former president of the Jewish Theological Seminary in the Hebrew Union College in Cincinnati, and renowned Jewish archaeologist, ‘In my opinion, every book of the New Testament was written between the forties and eighties of the first century A.D.'” (Source: Is Our Copy of the Bible a Reliable Copy of the Original?)