What color is your suncoral?
I have found that the orange ones are the most easy to get to come out to feed and are the easiest to bring back from near death. They will grow on just about anything (see picture with one growing on edge of old clam shell)
I am currently in the exact same predicament as you are with a black suncoral (the black color on its branches are wicking away - it hasn't come out to eat at all) - see picture
Typically, I will squirt a small amount of food around the coral (once they are feeding it doesn't matter if it is light or dark in the tank), to "scent" the water. About every half hour add another squirt of food. The food does not have to be meaty (cyclopeze tends to get lots of cyano in the tank when overfeeding); however, I find that certain meaty foods like mosquito larvae a.k.a. blood worms will cause the polyps to react quicker. (I actually like to feed my suncoral an algae mix that I also feed my fish and the sun coral loves it). It may take several hours for the polyps to extend the first few times you do this.
I have brought back orange suncorals that were down to the last polyp on a rock; however, it takes time to recolonize the rock. (see picture)
I used to move the suncoral to a round fishbowl for feeding - but it was quite tedious and I have since restored suncorals without removing them from the main tank.
I wish you the best of luck and I know how frustrating it can be. The black suncoral I have is a beautiful specimen and I shouldn't have believed the lfs when they said it was eating for them. It just goes to show that when you think you have figured it all out, you are quickly humbled.