If they're on the run or in brush, I like a shotgun, preferably small. Even trap loads work, but I prefer light loads of 5 or 6 shot. More fun than trap or skeet shooting if they're running.
If you can get them standing still a 22 is perfect for head or chest shots. Theres nothing to eat on the front legs around here anyway.
I really like light loads in the 357 pistol shooting 38spl on the run or standing still. Killed many
with that. In fact we ate 2 last week that was 38'ed.