Hollu ttree disease
Although it's difficult to tell for sure without seeing a sample from your holly tree, I suspect that the problem is an insect, cottony Taxus scale or cottony camellia scale, and the resultant sooty mold that grows following the scale. The sooty mold is a black fungus that grows on the honeydew or excrement of the scale insects. The sooty mold often follows the infestation by the scale insects, which are common in our area.
When the insect eggs hatch, a small active stage called "crawlers" come out and are then sensitive to insecticides or oil applied to the foliage. That is usually in June. At this point, you have probably missed the crawler stage, so you may want to use a systemic insecticide applied as a drench around the base of the holly tree. You could use dinotefuran, sold as Safari, applied according to the label.
Once you get the scale insect under control, the sooty mold will gradually wash off with rains. None of this will go away immediately after treatment, but will take some time.
Thank you for contacting Delaware Cooperative Extension,