My brother drops coons down in one shot with an airrifle. It is an old one, .22, 1000+FPS. He goes straight for the head from about 30 yards around the side of the house... or from his bedroom window.
There are powerful air guns, but the common ones you see aren't really powerful enough for one shot kills on something coon sized. That's probably because high powered accurate hunting air rifles cost way more than an equivalent .22 rifle.

There are powerful air guns, but the common ones you see aren't really powerful enough for one shot kills on something coon sized. That's probably because high powered accurate hunting air rifles cost way more than an equivalent .22 rifle.