In the states with big coyote populations you will see shotguns as well as rifles. The wide open western states with miles of Public Lands will allow for some real coyote shooting.
I shoot in a number of western states. I prefer the 25-06 and the .220 Swift. These are both proven old timers on the High Plains. Texas has a big kill each year. The states in the Northern Plains have big annual kills with no seasons or permits. The U.S. Fish and Wildlife Service puts Wyomings annual coyote kill at 50,000 to 80,000 animals per year.
If you like long range coyote hunting and want to prove your rifle spend a week on the High Plains.