Comparing a coyote rifle and an Elk rifle is like a golf cart vs. a four-wheeler...yeah, they're kinda the same, but one's got a LOT more power.

When you're wanting one gun that can do coyotes and deer or elk, you've basically got to get a relatively light elk gun...

So, really you're going to be looking at a .30-06 class rifle (.308, .270, .30-06, .257roberts, 6.5x55swede mauser, 7x5mm mauser), or a 7mm mag.

The 7mm mags are probably the better choice, although I'm not known for promoting them very often...they're flat shooting and throw small bullets, which is good for coyotes, but they've got enough stank for elk.

I'd personally recommend the 7mm STW, or WSM.

I'd get it in a standard weight rifle, it'll be a little heavy for elk hunting, but it'll be heavy enough to be accurate at long ranges for coyotes.