I am a rimfire fan, and believe that some rimfires are good medicine for Coyotes. Although I have never bagged a coyote with one, there are plenty who regularly do.
The main cvaveat..is "shot placement", after all a good hit by a .22 magnum is more effective than a good miss by a 300WM.
While Probably not good for some of the western ranges, at usual distances in northeast woodlands, they work well.
While all rifles can be used here, most of our local coyote hunters use dogs and shotguns...planning on the dogs to arrange a "drive by" shooting
opportunity, some NE states require rimfire for much of that type shooting.
Here for instance, is a Connecticut man who uses a .17 HMR, an dis pleased with the results. No wimpy dog either, but large sized Northeastern yotes..
https://www.youtube.com/watch?v=_PumRBMQ1lU As a youth, I hunted some domesticated but gone feral dogs that were cattle killers. I used a .22 LR, but it usually took more than one to put them down for keeps, so a fast repeater would be helpful in that case.
As I said, I have not shot any coyote personally with a rimfire, but I did take a good sized fox with my .17 hMR... About 100 yards,
one 17 gr V-max into the 'boiler room' and he simply dropped straight down ..DRT..