Yes a 22 mag would do the job if the beaver is on the bank. i grew up in kentucky and trapped most of my life there. unless the law has changed only the landowner can kill wildlife that is causing damage to the property. just being present isn't causing damage so legallyyou can't do anything till they build a dam.otherwise you can be fined forillegal taking of wildlife.
I trap 30 to 50 beavers a year a 330 at the dam crossover is the best set i have found.l