I lived in Japan for two years and have studied Japanese for 4 years. I love the Japanese and they have a great sense of humour. But it is very different from the western sense of humour. They do not really have irony as we understand it.
My wife (Japanese) says that it’s hiniku (皮肉), (if that doesn’t show up right, it’s the kanji for skin and meat) but I don’t think that’s correct. Every time I’ve heard hiniku used, it’s meant something more like “sarcastic”.
Perhaps related to blinkingblinking’s point about Japanese humor, it took her a few minutes to come up with any word for irony at all. Also, the only times I’ve even heard hiniku used is by other foreigners, or from a Japanese person commenting on something a foreigner said.