When does your coyote season start and end? Do you already have a place to hunt coyotes?
Like Nomercy, I also have a Ruger Mk II handgun in .22LR. I really like handguns and rifles in .22LR. Great caliber for learning and maintaining the fundamentals of shooting a handgun, and the ammo is the least expensive you will find. If your local laws allow semi-auto handguns for hunting, you may also be able to use if for hunting rabbits, squirrels, gophers and even coyotes if you have the skills and they are close enough.