score:12
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:
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.