I did this for a while back when I lived in SD and I pheasant hunted a lot more. Seems yotes were always popping out of the sloughs we walked.
It works best if you have both a rifle and a shotgun you don't care that much about. I was poor at the time, so I had an Yugo-surplus SKS and a Benelli Nova.
I had the rifle slung across my back using a sling with QD attachment and the shotgun in my hands. When I'd see a yote, the shotgun got dropped on the ground and I'd hit the button on the sling to release it so I didn't have to try to pull the whole thing over my head. It didn't always work, and can be annoying to carry, but if you like shooting coyotes as much as I do, its better than hoping your shotgun will make a vital hit at 60+ yards (it won't).
Depends on the terrain, but open sights might be best. If you walk any cattails, a scope will be full of fluff.