Just a few days ago i shot a raccoon with a daisy 1880 pellet gun right in the eye and he died and none of my neighbors heard it luckily because i live in a suburban area. So it is possible to do so with only a pellet gun.
They can be hard to kill, I wouldn't use a body shot with subsonic ammo if you have nearby neighbors; they might find one dead on the front yard.
If you shoot one in the head and don't see the hind legs kicking, you probably just knocked it unconscious.
Raccoons are very strong, I've had one tear the sheet metal top out of a havahart live trap and escape. I usually use a foothold trap, or the xl size box trap with a spring-loaded door: http://www.havahart.com/store/live-animal-traps/1081