We use a shotgun in open country to take coyotes, it doesn't have to be thick cover to use a shotgun on coyotes.
When we first started calling coyotes in 1983 with cassette callers we had quite a few coyotes run right up to the caller. They would smell the caller when they got to it and they would then turn and run off.
At that time we didn't know that you could "WOOF" at them to try and stop them. So quite a few coyotes that came all the way in to the e-caller got away.
So we started having a guy lay down about 15 to 20 yards from the caller with a shotgun. It worked good but was not very comfortable. So we came up with a camo pillow to put under our heads when we were laying on our back with the shotgun on our right side. The pillow has to be big enough and firm enough to prop the shot-gunner's head up so he can see.
The above picture is what it looks like with a shotgun guy using a pillow. We normally have a rifle shooter laying prone back behind and above the shotgun shooter.
The shotgun shooter can't see that well but he doesn't need to as long as he is looking towards the e-caller and doesn't move.
Quite often when laying down this close to the e-caller the shotgun shooter will hear the coyote's feet hitting the ground before he sees the coyote.
When laying down like this or laying down prone with a rifle most of the coyotes are not very concerned when they look right at you because your profile is so low to the ground.
You can also use the firm pillow to lean against brush so you can lean back into it. It gets your head up a little higher, so you can see better and it is more comfortable than not using a pillow.
In the above picture you can see the shotgun shooter on the left laying down. In the middle of the picture is my Foxpro e-caller and on the right is a coyote.
In the above picture the shotgun shooter is leaning into a bush and has just shot at this coyote. You can see smoke by the shotgun and a green Rem empty hull in the air about 2 feet to the right of the shooter. So the Rem HD BBs are between the shotgun and the coyote.
This is the next picture, just after the BBs found the coyote.
In this picture my son Wes is just sitting up from laying down with the pillow.
The shot just hit the coyote in this picture.
In this picture you can see that there is no cover for about 2 miles and the shotgun put this coyote down from about 25 yards away. The rifle shooter got to watch it all take place.
When using a shotgun like this along with a rifle shooter to back up the shot gun shooter we don't try to stop the coyotes. If the coyote stops in good rifle range the rifle shooter shoots the coyote. If the coyote hard charges right up to the e-caller the shotgun shooter stops the coyote with his shotgun.
Some coyotes feel perfectly safe in wide open country with no cover. If you stay low enough so your profile is 20 inches tall or less they are not too concerned about what you are.