How do I get rid of a coyote inside a city?

Assuming animal control won't take care of the problem, I'd suggest using a live-trap (so you can avoid injuring neighborhood pets) to trap the critter. Once you have the problem coyote you can either take him out of the city and shoot him or drown him.

Call the animal control, if they fail to do anything, get some antifreeze make sure your friends animals are inside then put it in a bowl outside at night, the coyote will drink it and kill it, so will most any other animal which is why you let your friends and neighbors know this.

Call animal control.

if it's actually in the city, call animal control and they'll take care of it and it's the city that needs to pay for it.

I see no other way around it, you can't shoot it and if you live trap it, what are you going to do with it?

PS. if you didn't know it, Newell's a troll that tries to get members in trouble, just ignore his answer, he's looking to get you in trouble for firing a firearm within city limits.

Law wise you prohibited from doing anything. It is illegal to shoot it, poison it, trap it, run it over, or anything at all whatsoever. You can't do jack until it kills a kid.

Your local DNR office has traps they can set for it.

Bait it. Kill it on your property (preferably behind high walls) with one shot of something quiet. 22 short out of a long rifle barrel?