I have had a similar problem with coyotes, but I don't live in town. However, I do have distant neighbors, and we have a gentlemen's agreement not to hunt. I shot at them with #9 birdshot for several years and they would leave for a while. One morning I watched them as a team, try to lure my big male airedale outside his invisible fence perimeter. He would charge them, but break off as he approached the barrier. They would circle back and try again. I decide right then it was "game on" and declared war against coyotes. I was being woke up nearly every night, right outside my window it seemed.
After some research, I decided on a .17 HMR. It is a 22 magnum load with a .17 calibre expanding bullet. I ended up with a Henry lever action and a 3 x 9 scope. So far, there are 5 less coyotes (3 bitches and 2 males) than there once was, and I think they got the message. I rarely hear them at night and never see them on my property.