Mike: You may remember a while back the post that raised the controversy about cougars and the 22WMR. I posted a pic of my buddy rancher that has killed well in excess of 200 cats with his Marlin 980DL in 22WMR, so as the cat is much harder to anchor (in my experience) than any coyote, I'd triple the vote for the 22 Mag on coyotes from 'resonable' ranges.
As with any question of this nature, it's shot placement that determines effectiveness much more than caliber. I say grab that 22 Mag and proceed with confidence.
Sidebar: I talked to a buddy yesterday that had just returned from desert mountain mule deer hunting here. While hunting, his buddy called him on the radio to tell him a "coyote" was uphill from him in the canyon at 20 yards. A minute later he called from about 800 yards away where he was sitting, and said that the 'coyote' was now
20 FEET from him..."turn around and shoot him!" He did, and the 'coyote' was a full grown tom cougar getting ready for the final pounce of his stalk. Whew, a close call to be sure, and a reminder to always pay attention when in dangerous country where these large cats prowl. He's having the cat made into a rug, as it suffered a fatal wound from my buddy's .270 Win on that hillside. Never mind that fact that he also had his .45 on his hip.....not enough time for the handgun, the rifle was in his hands. Be aware of your surroundings.
