Black spots on your plumerias may be a sign of fungal infections like blacktip fungus, Plumeria rust, or sooty mold. Pests and poor environmental conditions may also cause it.
If you find fungal infections, stop watering your plants for a while and trim off all affected leaves. Then, expose your plumeria to a lot of sunlight and spray its soil with a fungicide solution.
You can quickly remedy a pest infestation by rubbing or spraying the leaves with a mild insecticide.