I'm not sure why nobody else has mentioned this yet, but legholds/snares/conibears and urban areas don't mix. All it's going to take is someone's precious lap dog breaking its leg in one of your traps and you'll be in a world of hurt. You WILL hear the phrase "God forbid my toddler had accidentally been hurt"... Urban areas are dang touchy. Even if nothing runs loose normally, all it takes is a dog getting off the leash or out of a back yard to ruin your month.
Beyond that, it's getting more and more common for municipalities to have code preventing trapping within city limits, or even proximity code for how close it can happen near homes.
Further, you'll need to be sure your neighbors that might witness your "pelt friendly dispatch method" aren't even remotely squeamish, especially for a large animal like a coyote that takes a little back strength to dispatch "manually". Club a dog in front of the wrong people and you'll set some phones ringing.
Moral of the story, trapping urban coyotes can be tricky. The ONLY traps I use in town are live traps. Doesn't hurt anyone's pet, lets me take the animals out of town before dealing with them, and gives me the opportunity to get more permission by telling the landowners I'll be relocating the animals (I don't LIE and say I won't kill them, I just say they'll be captured live so I can move them out into the country where they won't be able to cause problems anymore).