For coyotes....
For coyotes I would recommend the 223, and I say this as a very satisfied 204 shooter.
I love its flat trajectory for gopher shooting. On a target with a hit zone the size of a soda can the flattest trajectory possible is a real benefit when you are not so good at distance estimation like myself. Where as a coyote has a larger kill zone, so being a little off on range estimation is not as critical.
The slightly less advantageous trajectory is outweighed by the vast bullet selection available to the 223 calibers as opposed to 204 (selection is getting better but still limited.) Plus if you don't reload, you can shoot the cheap surplus ammo if you go gopher shooting or to a range and go through well over 100 rounds in a day and not break the bank.
yes I am leaning to the 223 with a LTR ish 20"tube just lighter....
a 3.5/10 power Mark 4 on it......or Falcon menace
I'm no expert but this is exactly what i would do.
A nice sporter barrel, my 26" varmint profile is dang heavy when walking in snow to a good site. 12 lbs is nothing when at a bench in the back of a truck, but on foot in snow I nearly left it against a tree more than once on my way home.
And a reasonable magnification scope, 6-18 power is fine for gophers out to 350 yards but even down on 6x that was to much magnification when I called a coyote in very close. (seen nothing but grey hair, so took the shot and hit spine, the varmint bullet ruined the pelt) A typical 3-9 power scope would be better especially if keeping below 300 yards