I think you might have some disgruntled neighbours if you use a gun. I don't know how close they are mind you. Your choice ultimately. I would never encourage anyone to break the law. I wonder what is so offensive about using a crossbow?Yeah I would rather shoot them with a bow "illegally or not" than drown them.
Raccoon and coyote may be taken on private property by a property owner or designee all year if they are doing or about to do damage on private property. A license or written permit is not needed.
It says I can shoot it with a 22 but I dont know about that being in the city