I don't own a centerfire rifle specifically for coyote hunting, but I've worked up coyote loads in my three favorite deer rifles: 90 gr 270 WIN, 85 gr 260 REM, and 80 gr 243 WIN. When I go out for coyotes I carry the 243 or the 260. I haven't owned the 243 long enough to work up a load in lighter varmint weight bullets, but the 80 gr loads my 10 year old granddaughter shoots are just fine for yotes in the close-range places I hunt.
I suspect more people in TN use the 223 for yotes than any other centerfire cartridge, so that would make it "most popular".