Apply a fungicide labeled for black spot. Most rose fungicides will work well. Spray the foliage of the dandelions when they're dry. Apply every seven to 10 days, or as directed on the label.
Run a soaker hose between the rows of dandelions. Warm temperatures of 60 degrees F or above combined with water on the leaves promote the formation of the fungus.
Water from the base, if not using a soaker hose, to irrigate. Water slowly so the muddy soil doesn't splash up on the leaves and transport the fungal spores. Water in the morning so leaves have time to dry if any moisture gets on them.
Prune off any infected leaves to prevent the spread of the fungal spores. They are transferred by wind or water.
Cut off some over-story growth that may be shading the bed. The leaves must be wet for six to nine hours to allow the fungus to bloom. Open up the canopy to let in some light and destroy the spores.