Are you sure it's non-lethal? A bird hit with a pellet rifle could escape and then die later. Birds, especially flying ones, aren't durable. The eyes and skull in particular are vulnerable.
Birds of prey are illegal to kill, for good reason, and so are the vast majority of US native birds. Find another solution, you can get in serious trouble if you do manage to kill it, and that's not going to fix the problem of there being birds of prey in the area.
If you live in an area with...