The smell of a dead coyotes hanging from trees aparently scares them away, PO'd the wife too.
Was POing the wife a collateral benefit?
I would check the laws before shooting anything even pellet guns, crossbows, wrist rockets, paintball guns, etc. As someone else said, a lot of municipalities define firearms very broadly.
Trapping and calling animal control for removal would be one of my first choices. We have coyotes behind my house were there is a power line easement and walking/jogging/bike trail. Its is pretty dense suburbia though and they haven't become a problem, but I have a fenced in yard. I occassinally see them outside the fence looking in at my dog, but he's pretty big so I'm not really worried. They have never been agressive.....yet. They do keep the cat population down.