That stuff is called "peony measles" and it's generally the first stage of leaf blotch, a fungal disease of peonies.
Don't worry, it's not a serious disease, but it will make your peonies unsightly as the season progresses.
Right now you can do two things. First is to stop all overhead irrigation: like so many other fungal diseases it thrives when the plants are sprayed by water. Second, use a fungicide. Personally I avoid using copper on peonies because it can cause leaf burn on some susceptible cultivars, so I'd advise using one containing mancozeb, maneb or daconil. They all work well.
Finally in the fall cut all stems to the ground and dispose of them. Do not throw them in the compost heap: burning or burying are the best options. Rake the ground to eliminate all vegetable detritus and in the Spring, when the plants are growing again, apply another fungicide treatment.
