A 243 would be a good choice with plenty of longer range capabilities. If you are going to be hunting in very windy conditions, with long range shooting, you may wish to go to something that handles a heavier bullet than the 243. Many.many choices then, mine woulde be the 270
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.