Tunes: Jesu, Joy of Man's Desiring

It isn't remotely Irish, but Jesu, Joy of Man's Desiring, by J.S. Bach sounds really nice on the whistle. Granted, it's such a lovely melody that it sounds nice on a kazoo, but in addition to being a good tune it's usually scored in G and fits almost entirely in the whistle's range with little modification, so it's a good pick if you're looking for something different to play.