Let me clear up a great misconception. Coyotes do not LIVE in "dens". Coons maintain some sort of shelter, as do foxes. Tree squirrels, ground squirrels, prairie dogs, ground hogs, all maintain a year-round "home". Coyotes do not. They are well adapted to living in the elements, and do not require a "roof over their heads".
About 3 weeks, or so, before giving birth they will excavate a suitable "nest". It can be a brush pile, an old badger hole, a collapsed barn, rock pile, or whatever they can find that they feel secure in.
This, and only this, is what's refered to as a coyote's "den".
The breeding pair of coyotes are the only inhabitants of this den. Unpaired, non-breeding coyotes DO NOT DEN. They have no reason to, since denning is ONLY a function of pup rearing. Once the pups reach about 7 weeks, the entire family abandons the den, never to return.
The following year, the breeding pair "may" return to the same area. They "may" even use the same den, but usually not. Most will prepare a fresh new den for the new litter of pups.