Due to our law in SC we have to use a rim fire on fox, coon and bobcat at night so I go with the 22 mag. or shotgun with BB's. No pelt damage that amounts to anything and sweat little rifles.
I would say 22 for closer and 223 for farther with a lighter round. 22lr has worked for me with no exit wound, but thats just my 2 cents. kinda depends on the range of shooting.