I did a little reasearch on trapping mountain lions and it appears some folks out in Washington State may can help you, just read the some of the links this one gives you, they give contact information on how to use these traps.
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.