These things are pretty hardy if you isolate the affected tissue - I usually do like Tim and Richard said and cut away healthy tissue and make new frags - a quick bath in a lugols / new sea water solution with a small powerhead works wonders at getting rid of any remaining bacteria.

Although we don't often it is a really good idea to quarantine new corals just like fish - I have paid the price recently with a rock I got from a local store here that had something funky on it that grew and turned into a nasty brown jelly infection which damaged a nearby trachyphyllia before I discovered it in my nano. I won't mention the store's name but suffice to say anything I buy from there in the future will get an extended quarantine and / dip.