Hunter Customs,
I've had my best success with a FoxPro Wildfire electronic caller and a MOJO Critter motion decoy. Coyotes hear the call and when they see the decoy, they know where to go. Calling alone can work, but when the coyote has something to associate with the sound, it certainly draws them out into the open for a shot.
The advantage is having the caller and decoy 40 yards or so, away from your location, thus allowing the shooter to go undetected.
As far as rifle calibers, I prefer as much rifle as I can accurately shoot. If saving the pelts is a concern, just shoot them in the head. I switched from a .223 to a .25-06 and have yet to lose a coyote.
Bowhunter57