Coyotekillingfish, before we talk about "what rifle", we should talk about some basics of coyote hunting. Rifle choice is an outcome of the hunting requirements.
First, to be blunt, forget all this "long range" stuff. You have to walk before you run. Most hunters vastly, vastly underestimate how difficult it is to make a killing shot, from a field position, at even 250 yards, much less 700.
I've see a lot of guys showing up lately at the gun club with all the bling-bling shouting that they are all in on this "long range" fad. Thing is, when I look at even their 100 yd groups off a cement bench, most of these fanboys aren't even short range hunters, much less long range ones. And it only get's tougher from there because nothing in the real world is as easy as it is shooting off of a stack of sandbags on a comfy bench.
My advice would be to focus on the average if you want to kill coyotes as opposed to just scaring them. Get a rifle that's set up for your hunting and your capabilities and go from there.
The goal in coyote HUNTING is to call them in close and kill 'em the first time. Nothing makes a coyote harder to kill than one close call with a hunter. Bottom line is start by learning all you can about hunting and set yourself up for the closest shot possible.
As far as rifle selection, I would second the recommendation for a .22-250 if this is to be a "coyote only" rifle. I have several of these rifles and I've shot them hard on the varmint grounds in the west and they are fantastic rifles for the dollar. They can be upgraded later with aftermarket parts like a Boyds stock and Rifle Basix trigger to make them even better.
The scoped combos are within your budget range and that's a good place to start. If you can find the Axis 2 within your budget, that will save you from having to upgrade the trigger later.
Grouse