Holly is susceptible to a fungal disease called tar spot. The disease isn't fatal to the holly, and so is best controlled by hygiene, Remove and destroy badly spotted leaves, prune to improve air circulation and overcrowding, and clean up and destroy fallen leaves. Bag and burn the debris. Don't compost it since the fungus may survive composting. Clearing out the infected leaves prevents the disease from sending out spores to infect more leaves. The fungus likes wet leaves, so do what you can to help the leaves dry after a rain, and water only at the base of the plant. Also, mulch to keep soil from splashing up on the leaves.