Coyotes shouldn't be a problem unless they're sick or rabid. Otherwise, they should mind their own business.
However, this gives me another reason I can tell people when they want to know why I feel the need to carry my Glock with me wherever I go. I live in Athens, GA, which isn't a real big city, but it's not a small village, either. One night, as I was driving home, I saw the weirdest looking dog I had ever seen running down the middle of Milledge Avenue. As I got closer, I realized that it wasn't a weird-looking dog, but a perfectly normal-looking grey fox. I followed it for a couple blocks, trying to figure out where it was going, before it gave me the slip.
As long as they stay shy, no problem. That fox will just keep eating trash and dog food and the occasional squirrel or stray cat. However, if one goes rabid, they become highly unpredictable and dangerous.
Have we had a "what caliber to use on rabid coyotes" thread yet?