There's an abundance of humorous graffiti the ruins of Pompeii. It's dated at AD 79, but close enough that you may find it interesting.

Here's a couple of my favorites translated to English:

The one who buggers a fire burns his penis.

We have wet the bed, host. I confess we have done wrong. If you want to know why, there was no chamber pot.

I'd have a look at Mary Beard's "Laughter in Ancient Rome". Not only does she give some good Roman jokes, which are actually startlingly similar to jokes from today, she also goes into an in depth discussion of what the Romans thought about laughter in general.

There is a Greek jokebook from the Roman period called the Philogelos, or Laugh Lover. Here is a page with quite a few examples. A quick warning, though, is that the jokes are bad. Like, really bad. They are the sort of jokes you find on Popsicle sticks and laffy taffys. A few examples (lightly edited):

A yokel saw a eunuch talking with a woman and asked him if she was his wife. When he replied that eunuchs can't have wives, the yokel asked: "So is she your daughter?"

Someone needled a jokester: "I had your wife, without paying a dime." He replied: "It's my duty as a husband to couple with such a monstrosity. What made you do it?'

An incompetent schoolteacher was asked who the mother of Priam was. Not knowing the answer, he said: "It's polite to call her Ma'am."."

A misogynist was sick, at death's door. When his wife said to him, "If anything bad happens to you, I'll hang myself," he looked up at her and said: "Do me the favor while I'm still alive."

This next joke has always sort of floored me:

A doctor was talking to a patient. "Doctor," the patient says, "Whenever I get up after a sleep, I feel dizzy For half an hour, then I'm all right." "Then wait for half an hour before getting up," said the doctor.

Literally the oldest joke in the book.