We just had new stucco placed on an addition to house and have tried to put primer on with brush but the stucco is just too coarse for this method. Is spray painting my only option? Since the stucco is very coarse is “back brushing” still necessary because I don’t think the roller will penetrate the depth of the stucco?
"Back Brushing"? If you mean "Back Priming" … it's not possible with stucco since the back side is unreachable… Just roll on your primer with a 3/4 inch nap roller cover, it will do the job required… the stucco is not penetrated, it just gets a film primer coating that bonds to the surface… but more importantly use an exterior masonry primer!
Finish coat by rolling a high quality exterior product like Sherwin Williams A-100 … for stucco, a flat sheen finish looks best! Good Luck!