Here's a passage that indicates that God (specifically Jesus) made and sustains humor:
For by [Christ] all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities—all things were created through him and for him. And he is before all things, and in him all things hold together.—Colossians 1:16-17 (ESV)
Perhaps this is a bit of morbid humor on Jesus' part:
And he said to them, “When I sent you out with no moneybag or knapsack or sandals, did you lack anything?” They said, “Nothing.” He said to them, “But now let the one who has a moneybag take it, and likewise a knapsack. And let the one who has no sword sell his cloak and buy one. For I tell you that this Scripture must be fulfilled in me: ‘And he was numbered with the transgressors.’ For what is written about me has its fulfillment.” And they said, “Look, Lord, here are two swords.” And he said to them, “It is enough.”—Luke 22:35-38 (ESV)
I'd call this famous sentence a pun on two separate axes:
And I tell you, you are Peter, and on this rock I will build my church, and the gates of hell shall not prevail against it.—Matthew 16:18 (ESV)
Besides the obvious Petros <4074>/petra <4073> pun, I think renaming Simon to "The Rock" is pretty funny given his often mercurial passions. Actually, Peter's interactions with Jesus often turn out to be comedic even if He is playing the straight man.
Jesus loved exaggeration:
Then Peter came up and said to him, “Lord, how often will my brother sin against me, and I forgive him? As many as seven times?” Jesus said to him, “I do not say to you seven times, but seventy-seven times.—Matthew 18:21-22 (ESV)
This is followed by the parable of the unforgiving servant, which is a tall tale if you know that 10,000 talents is an impossibly large sum. It's also a reference to Esther, which can be read as humorous. Jonah can also be read as satire and many of the provocative actions of the prophets are slapstick if you think about it. Remarkably, God is directing the action in these stories.
I don't know if one could say that the Jewish people invented jokes, but the Hebrew Scriptures certainly contain more than their fair share. (And rabbinic commentaries have no problem adding to the humor.)
But I think our best evidence that Jesus enjoyed a good joke once in a while comes from a story told by Luke and Matthew. After He reassured John that He was the expected Messiah, Jesus told the crowds:
“To what then shall I compare the people of this generation, and what are they like? They are like children sitting in the marketplace and calling to one another,
“‘We played the flute for you, and you did not dance;
we sang a dirge, and you did not weep.’
For John the Baptist has come eating no bread and drinking no wine, and you say, ‘He has a demon.’ The Son of Man has come eating and drinking, and you say, ‘Look at him! A glutton and a drunkard, a friend of tax collectors and sinners!’ Yet wisdom is justified by all her children.”—Luke 7:31-35 (ESV)
I don't think Jesus was joking in this passage, but He contrasts Himself with John, who doesn't seem like he was a lot of fun to be around. To me, it doesn't seem like Jesus would have been invited to very many parties if He didn't know how to have a good time with friends. And that strongly implies that He had a sense of humor.