A couple of fungal diseases attack peonies when the conditions are right--cool and wet. It is a good idea to remove and dispose of the affected plant parts immediately. In fall, after frost kills the rest of the plant, remove all plant debris from the ground. These fungal diseases (Botrytis and Phytophthora) thrive in heavier clay soils that don't drain well. If the soil in your garden is clay, it would be a good idea to dig the plants up, amend the soil in each planting hole with generous amounts of lightweight, loose compost, and replant. It's possible that the diseases won't show up again next year if the weather isn't ideal for them. If you want, you can spray the plants next year with a fungicide. It must be reapplied several times to be effective.