Since no one else has answered you, it looks like a blight that needs to be treated. To do that you would want to remove all affected parts of the plant. Here is a link

http://www.extension.umn.edu/distribution/horticulture/DG1153.html

From what I understand it happens during moist conditions. I would cover them during the hot part of the day with a little awning of some sort. If you do a search on these 4 things you should be able to get them back up and running. 1) Peony disease 2) Peony care 3)Transplanting peonies 4)Transplant shock. Google those 4 things and it will bring you a host of info. Read read read. Good luck.

They're fine....they were stressed from being newly planted. Peonies are tough!!...They have survived for 100 years in abandoned homesteads and overgrown cemetaries.
Linda C

I agree your problem is stress from planting in the heat of summer without providing shade for a week or two to allow the plant to adjust to the transplant. With a few days of sun protection your peony will be fine. Al