Most areas around there private property at least to the eastern plains. Ft. Carson I believe offers access to some parts of the post for hunting. There's some pretty choice coyote and bobcat terrain on there. If you're willing to drive some there's the Commanche Nat. Grasslands down by La Junta.
When calling coyotes, more often than not they will circle on a target they are
coming into and approach from the downwind side. Presumably they do this in
order to align what they smell, with what they are hearing.
This means that you should always have your downwind side camouflaged and have
an open shooting lane. If the area is heavily covered the coyote could come in
take a look and be gone, with you none the wiser.