Is there anything that is attracting the tang? My
blue tang started nipping at my clam. It ended up that there was a sessile snail on the clam (the kind that make the spider web looking mucus to catch stuff in the water). The tang was going after the stuff caught by the sessile snail and nipping the clam in the process. I pried it off the clam and the tang was still nipping because it remembered it being there. So I moved the clam a few inches and the tang forgot about it.
So anyway look to see if something is under the coral or if food is getting caught in it that is attracting the tang. You also may need to move the coral to make the tang forget about picking on it.