I killed tons of grouse and many rabbits with a Crosman pump .22 cal. (I forget the model number). I still have one of the camper models with the interchangeable stock and grips. Use oil sparingly but regularly, and they will last you for years and years. Use the best pellets you can find, and have fun.
For many years, I used mine on Thanksgiving day to go out and get grouse for my Thanksgiving supper. We would be camping out at our moose hunting area, and I would get several ruffed and/or spruce hens. I would also pick wild cranberries for cranberry sauce, and, most years, I could get wild mushrooms. made a feast of it every time.