You have any suppressors? That could dictate what caliber you run.
If not you may consider the distances you would be shooting coyotes at. Location and terrain local to you combined with specific hunting sites should be considered.
Everyone has opinions about distances and ethics....let's not derail this thread with that.
If I was going to be shooting past 400 yards regularly at coyotes I would run a 6ARC or 224V if I was staying small frame and running a gas gun.
I built an AR a few years back that uses some quality parts where it really matters (bcm thermo fit upper, White Oak Armament SPR 18 in barrel, SSA-E trigger, jp scs H2, PRI gas buster, and adjustable gas block. The rifle shoots amazing.
I do reload but it's really awesome to snag IMI razorcore 77 gr and 69gr when it goes on sale with free shipping/no Hazmat.
I have yet to take it out coyote hunting but in 2 weeks I am doing a local coyote competition.
If you don't have a large frame gas gun and have other potential needs/roles it may be worth considering a large frame even though it's definitely not required. A 6CM or 6.5CM would be a sweet rig to really hammer down and be able to deliver energy at longer distances when needed.
Good luck, it's a tough time to be buying or building right now.
There's a bunch of quality manufacturers that make what you are looking for.
Buying an MK12 upper and an SSA-E for a lower you have is another way to get the job done. I know you said you don't wanna break up a rifle but I have seen MK12 uppers for sale here in the px frequently as of late.