I would second MB on his recommendation of a catapult or "bean flip."
Easily home-made, using the fork from an apple or other suitably shaped tree branch, surgical grade rubber tubing, the tongue of an old shoe and either braided nylon fishing line or dental floss. SG buckshot or 10mm steel ball bearings are very effective on rabbit-sized game, and with practice you can shoot accurately to 10-15 metres.
My boyhood example is used for whacking bears out of the vegetable garden.