The only evidence I know is their assumption that no body could not possibly have predicted the fall of Jerusalem. Hence, Jesus could not have foreseen the destruction of that temple.
The problem with that assumption is, that it's "the one million dollar question". Christianity believes that Jesus is God and hence could have easily predicted the event. Now, I am not saying that Jesus is really God, that's something I want to know my self.
However, those who argue for a latter date is trying to discredit christianity. Trying to disprove christianity by assuming the christians were false is kind of circular. Hence I need more evidences.
Moreover, Jesus may not be only one that predicted the fall of Jerusalem.
But, what is still more terrible, there was one Jesus, the son of Ananus, a plebeian and a husbandman, who, four years before the war began, and at a time when the city was in very great peace and prosperity, came to that feast whereon it is our custom for every one to make tabernacles to God in the temple, he began on a sudden to cry aloud,
"A voice from the east, a voice from the west, a voice from the four winds, a voice against Jerusalem and the holy house [i.e., the temple], a voice against the bridegrooms and the brides, and a voice against this whole people!"
This was his cry, as he went about by day and by night, in all the lanes of the city [Jewish War 6:5:3].
Note: That being said the story of Jesus ben Ananus is also written after the fall of Jerusalem
However, Luke didn't mention the death of Paul, etc. Suggesting earlier date. So which one is right?
So, assuming Luke is honest, another big assumption, people think that Luke is written before the fall. If Luke is written after the fall, surely he would write about Paul's and Peter's execution. This suggests much earlier dates.
What are the other evidences that support the latter date theories? If you want to add supports for the earlier date theories it'll be great too for comparison.