Weasel - The quiet gun question comes up every once and a while. Usually in situations like you discribe. Since we can generally cannot use silencers on our weapons to hunt with, a quieting device is out of the question. With that aside there are some muzzle breaks that have the ability to redirect and disperse sound along with the spent gas. I don't know which ones these are but I've heard about then. They generally take the pattern of a tank muzzle break.
Lets place this option asside. Some priciples need to be understood. Long barrels are quieter that short barrels. Big cartridges are londer than small ones. So to have a rifle be as quiet as possible you need to be shooting the smallest cartridge that can get the job done through the longest practicle barrel. The little guys that we are talking about are one of the wildcat .17's, 22 hornet, 22 K-hornet (an improved 22 hornet), 221 fireball (this would be my choice in a quiet effective round, but an expereinced reloader option only), 222Rem and 223Rem. You've severely limited your choices if you insist on having a semi-automatic. In the practical semi-automatic arena you are basicly limited to the AR type rifles in 223. Another thing comes to mind. 7.62x39. These are small, accurate and fairly quiet. But again limited in supply if you want a semi-auto.
I have a predjudice toward a bolt action rifle if you are trying to keep as many options open as possible. Go for the bolt and make every shot count. Sprayin' and playin' is a great deal of fun, but do you really need it for coyotes?
I've got a friend that is working with just the rifle for your application. It is truely a rifle experts round and right out of the box it is scarry quiet. He took a 700 action, screwed on a fairly short 30 cal. douglas barrel in a fast twist and chambered it for a variation of a 30 whisper. He loads 200 or so grain bullets and tinny amounts of powder in a much shortened 223 case and punches little groups. I think that if you were quick you could catch the bullet in flight. Now theres a quiet round and I have no doubt that it will kill coyotes.
Michael