It could be peony peony measles (Cladosporium) due to the spots on the stems. But, It also looks like it kind of got fried on the black plastic. I'd get that black plastic away from it as soon as possible. Cladosporium won't kill your peony but you should dispose of all the diseased leaves and stems away from the plant and don't compost them. Here is some information on Cladosporium.
http://hyg.ipm.illinois.edu/pa...
