I experienced something like this before... some kind of brown coral disease... i found an iodine dip to be particularly effective. The corals dont seem to be too bothered with iodine, but it was able to eradicate the disease. I used the Seachem Reef Dip, and as per the instructions painted some pure undiluted reef dip solution onto the affected areas. The brown slime/disease went away within a week. But a dip should work fine too.
You will need to have a way to remove the corals from the tank for the dip though.