Everyone forgot the Condor .22 or .25. A Condor 25 can equal or best many .22 subsonics on the market and can shoot 43gr pellets or heavier. They have .25 Barnes 67, 78 and 90gr slugs that many guys shoot out of their Condors and get 115 fl-lbs of energy or more. I get 90fpe with just 43gr .25cal pellets, and 79.5fpe (almost 80) with 31gr Kodiaks.
I can easily shoot a 31gr .25 Kodiak through a coyote's skull beyond 30yds with a muzzle velocity of 1,060-1,070fps (subsonic). If I can get passthrough on racoon and possum (and G-hogs at 35-40yds) with a 21-22fpe Diana 350 .22, a Condor .22 or .25 will have no problem going through a coyote's skull at greater distances But it doesn't have to. You don't need a passthrough to kill one, and you can always try and take a frontal shot. A "between the eyes" shot would guarantee a kill.
I am not saying the .22 subsonic is not a good idea but do not underestimate it. I praised the .22 subsonic and said it was a good choice in my post earlier. All you really need is 13-14fpe on impact to the head, and the coyote is history. If people can take foxes at 15yds with a 34 .177 (posted here several times, and even a coyote with a Panther 34!) which is 14fpe at the muzzle (900fps), then you don't need 8 or 10X the power for a head shot on a coyote, but the more power the better of course
A good 20+fpe Magnum Springer will do the job on a coyote with a well placed shot to the head inside 30-35yds. It's been done before, nothing new, but if the Coyote was beyond 30yds, I 'd use a more powerful (>30fpe) PCP for peace of mind. Since there are not too many PCP's that go well above 30fpe, or cost $1,200-2K because they are European, the best bang for your buck is a Condor or a Talon with a 24" barrel. Standard Condor (no mods) - 50-60fpe depending on pellet weight, and Talon 24" 35-40fpe. If you can legally shoot firearms around the neighborhood or suburbs, then a $200 .22 rimfire rifle is your best choice, give or take $50-100 if you want a really nice one. For me knowing I can take any size animal up to and including Coyote with a small bore Airgun is priceless

Just ask that fox from 2 months ago

I 'd say the fox's head resembles the Coyote's a lot, and is only about 25-30% smaller. If you can drop a fox dead in its tracks, you can be sure you can do the same with a Coyote with a comparable shot and distance.