just like i said in the other coon post, dont be shooting a centerfire up in the air as most coons are in trees as far as i know
i say .22 or 12 or 20 gauge shotgun
I use a .22 LR - its plenty to knock them out of the tree. If they're not dead when they drop the fall usually does them in. Get a good light and go for a head shot 9 times out of 10 they're DOA
A .223 is going to going to produce a large exit hole. This will ruin the value of the hide. The .22 is all that is needed. The lighter weight .17 bullets will do the job nicely without ruining the hide value.
.22 pistol gives you a lot of versatility when you are huntin. you dont have to worry about hittin it on trees and stuff, just put it in a holster and your good to go.