Most any centerfire .22 caliber rifle will work fine. Anything shooting a 50 gr. or larger bullet will usually result in a quick clean kill, with the animal just going limp and falling to the ground.

Practice is the key. Get a gunthat fits youwell (because you'll have to sit with it aimed for long periods of time)with a good scope, and in a caliber you can afford to shoot. It doesn't do any good to get a new XYZ whizbangmagnum if shells are $20/box and you can't afford to practice enough to ever become a decent shot. I've got a .223, and I got it for that reason. I can afford to go out and target shoot frequently, and as a result I'm a decent shot with it. Its ballistics don't graph out as nicely as some of the other guns, but I haven't ever felt under-gunned when taking it out in the field. With a decent sized bullet, I have never lost an animal with a decent shot.