Well, first, I can not hit the broad side of a barn with a bow, and truthfully, a bow is a bit of overkill for small game. However, I have been using pellet rifles since I was a kid to take small game. And the newer pellet rifles, the gas springers, are powerful to take down a deer size animal at close range.
I have a cousin who lived north of Atlanta in a subdivision that backed up to a large game reserve. Squirrels had taken over and his wife got him a Gamo .177 springer with a silencer to solve the problem. Well, early one morning, he looks out the window and a big doe has jumped the fence and is eating everything he has growing. So he thinks I will pop her in the butt with this pellet rifle and she won't come back. He hits her in the butt, but that little pellet rifle shattered her hip and he has to finish her with a shot behind the ear with that pellet rifle. LOL, we grew up hunting and you just don't waste a kill, so he dresses her out and packs the meat in the freezer. The whole time he is looking over his shoulder worried about his snowflake neighbors. The point here is those little pellet rifles are packing a punch somewhere between a .22 Short and a .22LR, and are no longer a kid's toy.