I've never hunted the den, for some good(?) reasons. Waiting out a wild animal is nearly impossible. Coyotes come out when they want to and not before. Besides, you could be set up on an empty den. They may be out hunting already.
If you call one out of the den and shoot it, the rest will hole up for ever, or until you go away, whichever comes first. Plus, the sound of your shot has just educated the rest of the pack.
I'd set up several hundred yards away from the den when you find one.
My two cents.

critch