Shoot it through the lungs with a 40 Grain bullet from a sub-sonic .22 LR load and let it run off to die elsewhere, shoot and forget. I doubt that the authorities will do the forensics on a dead coyote and come looking to do a ballistics match of firearm to recovered bullet.
We have lots of suburban foxes, as the coyotes out-compete them in the country and drive them into the suburbs and city.
My former next door neighbor moved to a golf course development that protrudes out into farmland and before she moved, I told her not to let her cats run free or she'd lose them to the coyotes, 'cats, foxes, and big hawks that live in rural areas. I saw her at Wal-Mart recently and she told me that 3 of her 4 cats have "run away" since she moved. I didn't have the heart to tell her that they had probably been caught by a predator and being house cats, didn't know enough to run fast and/or climb high.
