The Colt made AR-15 is a well made rifle that should deliver all the accuracy you need for coyote under the conditions you describe. The 6600 version though, was I believe only offered with a fixed carry handle. That will limit your optics mounting options compared to a rifle with a flat top and a picatinny rail. Personally, I would look at the newer detachable handle, flat top models from quality makers like Bushmaster, Rock River, LMT, or S&W. A shorter, lighter weight barrel would make for a better carrying and handling weapon without any significant loss of accuracy or velocity.
The .223 and the 5.56 NATO are basically the same case, exterior dimension wise. NATO chambers tend to spec with a little more leade then .223 chambers. The NATO round is loaded to slightly higher pressure then commercial .223 ammo. Military NATO cases tend to be a little thicker and have harder primers then .223 ammo. Conventional wisdom is .223 ammo can be used in a 5.56 chambered rifle, but that using 5.56 in a .223 chamber could cause excessive pressure. Personally, I know a lot of shooters who interchange ammo without issue, as most any modern bolt action rifle can handle the slight pressure difference. I probably would be leery using heavy bullet 5.56 ammo in a rifle with a tight target spec .223 chamber, especially if the bullet was jammed against the rifling. Check the specs. of the rifle you are interested in to be sure, but most AR's are chambered these days to accept either round.
Larry