Some years ago, my father's friend Vic got tired of the squirrel in his feeder. As, I remember Dad telling the story. Vic used to be a machinist. He is a vetran of world war II. He died, some years ago. So, Vic's answer was to get his .22 rifle, and shoot the squirrel. Another squirrel came along, and also met his death. Vic gave up, after the 300th squirrel.
Folks will suggest various air, spring, or rimfire guns. Many people will have excellent ideas. To those, I wish to add the suggestion of trying to find a use for a continuing stream of dead rabbits. For, there will not be just one or two. Perhaps you can add "mystery meat" to the casseroles you give to widows and orphans? Perhaps you can clean them, and sell the pelts to companys that sell rabbits feet for luck charms, or makes blankets?
It may be a bit less noisy outdoors, if you keep the muzzle a foot or so inside the house when you squeeze em off. Telescope sight. Bench rest. Some internet research. Maybe brain shots. Set up a target in the garden, and adjust your scope. Since the range will be essentially the same each time, from the window to the garden.