I am just getting into coyote hunting in the mountains of NC. Step hills with tight valleys and shots under 75 yards.
I use a 12 gauge with 3 inch Hevishot= heavy recoil
I am considering installing a red/green dot or reflex sight.

Under $100
open or tube type?
brand?
pro and cons?

Any suggestions etc will be appreciated

I'd skip the red dot or any type of scope for shotgunning yotes. They'd probably be OK for a yote coming to a call. BUT, if the bugger gets in close and decides something ain't right and trys to skedaddle its like wing shooting and keeping him in a scope could be a real problem. When I'm calling I carry a 223 with scope for the long shots and a 12ga 3" #4 steel modified choke if one sneaks in close. I don't know how hevishot performs but with my rig 45yds is my max. If I'm gonna be shooting out to 75yds I'd carry the 10ga.

Point taken, after all, the shotgun pattern is more forgiving than a rifle. I do have open sights on the shotgun now. I still have to pattern my shotgun with the Dead Coyote choke and hevi shot 4 buck and T
At what ranges do you shoot at with the 223 and what power scope do you use?.

Generally 200 is my limit but if he's willing to come closer I let em. I use a 3X9X40