My three-year-old nephew tells this knock knock joke.
"Owl eating carrots!"
It's very funny. Try it. There can be variations to the owl. "Zombie" is pretty funny too. Though it is possible that these jokes are particularly funny because a three-year-old is telling them.
This kid likes to be funny. He does something silly and waits for the laugh. The other night, as I helped him on with his pajamas, he was making silly sounds. "Funny," he said, as he saw me smile. I nodded, a bit grudgingly. "You laughed," he pointed out. "I did," I conceded. "It was funny," I said. He smiled. That's all he was looking for.