When was the early Christian apology "Dialogue with Trypho" written? I recently became aware of the Dialogue with Trypho, a Christian apology regarding Jesus being the Messiah, written by Justin Martyr sometime during his lifetime (in the years 100–165). However, Wikipedia doesn't say more specifically when during his lifetime this apology was written. 

Have any historians more specifically dated Dialogue with Trypho?
Justin's Dialogue with Trypho is usually dated toward the end of his life, after AD 155.  According to Craig D. Allen, this is largely based on evidence that it was written after his First Apology, which can be dated with some confidence to 151–154.  The line of reasoning is as follows:


Justin mentions the First Apology in his Dialogue with Trypho, so the latter work must come after the former.
The First Apology calls Lucius Pius, born in AD 130, a "lover of learning" and a "philosopher," suggesting a date after AD 145
The First Apology mentions the popularity of Marcion, and he was in Rome between 139 and 142, again suggesting a date after AD 145
The First Apology makes reference to Felix the governor of Alexandria, who appears to have held office between 151 and 154.


Allen concludes:


  If 1 Apology lies between 151–154, and because the Dialogue mentions the Apology it is certain that the Dialogue was composed after that date.  Any conjecture regarding a more exact date than 155–167 is only that.  We must, therefore, be satisfied with an imprecise date for the Dialogue with Trypho. [Revelation, Truth, Canon, and Interpretation, 34]


That said, Susan Wendel suggests a tighter range, citing other scholarship:


  Scholars generally agree that Justin wrote the Apologies around 150–155 CE and produced the final form of the Dialogue with Trypho at a slightly later date (~155–160 CE). [Scriptural Interpretation, 11]


Wendel cites Eric Francis Osborn, who indicates the same range of 155-160 (Justin Martyr, 8) and Leslie William Barnard, who suggests circa 160 (Justin Martyr, 23).

So our best bet appears to be around AD 155–60, with a bit greater confidence on the first of those numbers than the second.