Please don't shoot the coyote! Most likely, if coyotes are truly hated where you live, someone else will do it for you.
Coyotes are part of the food chain and without them we'd probably have a terrible rodent problem. Do you want the countryside to look like the NYC subways?
We can't keep randomly killing animals just because they bother us.. there has to be an eco method that will stabilize the natural food chain. In the meantime, there's no reason why you shouldn't cover up that den & keep them out of your yard.
Check out this website to find out more:
http://www.projectcoyote.org/