12 gauge shotgun, Triple-B (BBB) Shot. You can find these in 2-3/4", 3" and 3-1/2" Magnum sizes at your friendly neighborhood gander mountain type store.
Geese are the only creatures I can say I'd kill out of season. When out of season, I 'hear' that a .22 works nicely.
All these friggin poop machine rats-with-wings need to go. We've got too damn many of them and a bag limit of 2 a day just isn't cutting it. I enjoy goose meat, however there is no way I could eat all that I bag, so I breast them out and donate them to a local food shelter. This is only suggested during hunting season, as if done out of season one may become suspicious of your steady flow of honker meat.