I have had similar issues with tree corals. The black spots will eventually be the start of the coral decomposing. When it happened to me, it was either an issue with water quality, another coral stinging it (torches, hammers, galaxia, etc), or water flow on the coral. Assuming that you have already checked your water parameter's and corrected any issues there, and that you would have already noticed if another coral was stinging this one, then the next step is to check the water flow. Coral's like these have a happy zone for water flow. Too much flow and the polyps never open and the coral eventually dies. Too little flow, then the coral can't shed it's skin properly and it decays. Ensure that the coral has gentle movement due to the flow, but not so much that it is being blown back. Keep in mind that as the coral gets more dense by the growth of additional arms, then a bit more flow is needed so that the water can get through (or thin out the coral). Adding Iodine will help the coral shed and it will help regenerate the coral tissue (hopefully you are already supplementing with Iodine). By doing this, small areas of decay may correct itself. If larger areas of decay are present, or the coral gets worse in some areas, then I recommend cutting off those pieces of the coral and getting them out of the tank. If you have leather corals in the tank, ensure that the shedding skin from those corals aren't getting on the tree corals (chemical warfare).