Rereading this thread reminded me of a few things:
If I had to settle on one all-around prairie-dog round, that also would work on coyotes at typical ranges, it would be the .204. But I don't shoot that many coyotes anymore, and still shoot a lot of PDs. This is because the .204 shoots so flat at "hittable" PD ranges--and I am among those who finds I can see the hit more often through the scope than with a .223. This may defy "recoil" physics, but there it is.
But after using the .204 as my main PD rifles for around a decade, now primarily use it for ranges of 250-500 yards. Out to 125-150 or so, start on PD towns with the .17 HMR, because the low report doesn't spook them nearly as much as a .204 (or .222, .223 or whatever--have used both a LOT).
Once all the 17 HMR-range dogs are dead or down in their holes, I switch to a .17 Hornet, which in my experience works great to around 250-300, depending on the wind--and also is enough quieter than a .204/.222/.223 that it doesn't spook them nearly as much.
For 300-500 yard shots I break out the .204, with 40-grain Hornady V-Maxes, which has the highest BC of any 40-grain plastic-tip in that weight-range. (And yes, I prefer plastic-tips, both due to higher BC and better expansion at longer ranges. Have tested this a LOT since the late 1980s, when Nosler Ballistic Tips first appeared.)
Don't use the .223 as much unless I come into some really "affordable" ammo with typical "varmint-weight" bullets in the 50 grain range. But do sometimes use the .223 as my 500+ yard PD round, these days with heavier, high-BC plastic-tips in my 1-8 twist Ruger American, which also has a 2.5" magazine length, due to the extension that Whittaker Guns sold for a while--and from what I understand, might again. But have also used several other cartridges for 500+ ranges, these days often my 13-pound Sisk Rifles 6XC with plastic-tips in the 90+ weight range.
But the landowners in the places I normally hunt want as many PDs shot as possible; otherwise they consider poisoning them. So I primarily concentrate on the higher-percentage shots under 500 yards.
