I started out with my 700 vsf bull bbl. 223 but after hauling it around im switching setups. My new yote toy will be a bushmaster h bar AR 15 with nikon camo 3-9x40 with extra high burris rings. Im changing all the furniture to OD. It will be lighter and better for follow up shots.
I had the same feeling as a lot of the guys. I went through about a 2 week stage where I was pretty much 100% sure that I needed to get a Savage 12FV or some other heavy barreled rifle to even attempt predator hunting. And, I'd need to top it off with a $500+ scope to be effective. Wrong... Got my CZ 527 American in .223 with a $50 NcStar 3x9-40mm scope, and it's all I need. Needless to say, I will upgrade the scope in a few weeks, but I'm satisfied with my setup.
I've never specifically gone coyote hunting, but I've shot a good number of them while out deer hunting. Especially out in Major county where a friend has some land. They just always seem to appear and I'm not one to waste an opportunity. Especially when it comes to eliminating something that is killing off the turkeys, etc.
I've used:
.270 Winchester = 6 yotes
30.06 = 2 yotes
.300 Win Mag. = 1 yote (pull the shot and hit him in the neck at 243 yards. Decapitated that one.