I have shot coyotes with lots of rounds, but my favorite '06 size cased for a long time was the .240 Weatherby. I used a Barnes 90X as an all around load, and it was pretty easy on coyote hides. The .220 Swift and 22-250 Imp were my favorite hot .22s ( I played with a 22/6mm awhile but shot no coyotes, too many surgeries at the wrong time of year then!)
The .270 became popular in Se Texas ( big woods/thickets) in the Browning auto and Remington pump in my neck of the woods. I used a .280, so had no use for one. I could never get used to the forearm of a any pump I tried (shot friends rifles) so they never appealed to me, although they shot well indeed. I worked with a welder in Texas as a young man, and he used a BAR in .270 with a 3x9, shot deer/hogs off pipeline right of ways, so I was intrigued with that. I bought this old BAR here in Utah from a retiring hunter (first owner) when my dad died (2001) I had some nice engraving done to that slab side, cleaned, nice reblue job, just as a memorial really but it turned out to be a gee wiz shooter! My next trip to Texas for exotics or deer it will go with me. It is a tad heavy for me to pack in the mountains, which I did in 2001, but only shot a jack rabbit with it. I went back to my old Whelen in its synthetic stock for the mountains, whew. ha .