I have shot woodchucks from my bedroom on the second story with a Sears Roebuck 22. The window was open so spooking was not to be had and that was in a situation where I really needed the food. This may be different.

You're most likely smarter than the bunny. You can devise barriers and shields. You can feed it some alternative food. I suspect that the bunny isn't going to hurt you in any way; it's just looking to eat. Anything. Maybe it has babies. Helpless blind babies. I think if you kill it you should thank its spirit and eat it. It's only fair.

You could also toss chicken carcases over the fence to attract coyotes.

Just sayin'...

Suburban rabbits tend to get used to folks so you likely could use a pellet gun. Poison is out for a number of reasons, mainly, as it dies it becomes easy prey for predators (including cats, dogs, hawks, etc) who then get poisoned.

tj