In an interview in Zeit Peter Handke says he's not funny when he wants to be and is sometimes funny when he doesn't mean to be.
He says he wrote one joke that nobody but he finds funny and that even worse, he always laughs aloud at his own joke, which no comedian should ever do.
Here's the joke, which I find quietly funny:
Also, es gibt doch das Gemälde von Caspar David Friedrich, zwei Männer in Betrachtung des Mondes, oder? Ich habe das Bild für mich neu gemalt. Ich sehe da einen Betrunkenen: einen Mann in Betrachtung von zwei Monden.
So, there's that painting by Caspar David Friedrich, two men contemplating the moon, you know it? I painted a new version. I see a drunk there: one man contemplating two moons.