I looked in my coral book (
Aquarium Corals, Borneman), but as I don't even have a coral in my tank yet, take my advice with a grain of salt
The book says you can either do a dip in Lougol's, or target drip some near the problem on the coral in the tank. It says some corals don't react well to the Lougol's, though.
From the pics in the book, it could be white plague, or possibly some other kind of necrosis. The other option it mentions is to do surgery on the coral, outside of the tank.
Maybe Google for white plague, and see if pictures match what you're seeing.