Years ago I used a 7722 in .22 WMR on several coyotes. I was hunting where the landowners didn't want a lot of noise. Not my best experience. It works if it's your only option, but even moving up to a .222 is highly preferable.
Just this summer I bought a Ruger American in .17 hmr. I will likely take a coyote or 2 with it but have not done so yet. I don't have high hopes for the cartridge on coyotes. Reports from trusted acquaintances tell me that it's a doable thing, but results are iffy.
When the opportunity comes I will shoot carefully and selectively.
