Seriously caliber/cartridges makes little difference I find a 222 Rem to be an ideal coyote killer same with the 20P as long as I put the first shot where it counts and not ask it to do more than it's capable of. A 223 is a dandy. Coyote cartridge I used a bolt 223 for 20+ (1966 to 1990 ish) years, just added another 223 to the mix last year. The 22-250 has been the go-to for coyote killing for 70 years, still with us and killing coyotes. If pelts aren't a big deal the 243, 6mm ARC or any of the modern 6s might be a choice.
You can get a 223 in a light rifle with a smaller action, Howa mini, CZ- 527, Mini Mauser. The 22-250 needs a fullsize short action Rem 700, Howa 1500 etc..