With my limited experience, that sounds like botrytis. I've had a similar issue with a few of my plants. Practice good sanitation. Place the debris in the trash and not the compost or lawn, and keep removing the noticeably infected parts.

Sorry, the site keeps telling me the links don't exist, so I'm just pasting them into the body of the message:

http://forums.gardenweb.com/forums/load/peony/msg051442519846.html?6

http://www.extension.umn.edu/garden/yard-garden/flowers/diseases-of-peony/index.html

Thank you! I googled after posting this and figured the same thing. The interesting thing is that only some leaves are affected on the plants, and only one plant was really affected, with the stem almost dying back to the bulb (so I guess I remove that whole stem if it's black?), but a new shoot is coming out from another area of the ground where the tuber is. I guess we'll wait and see. We've had SO much rain this spring and intense bouts of it that I think the ground was just so saturated recently, no chance to dry out even if drainage is good! Seems to finally be getting warmer, and the other plants seem to be doing well. Thanks!

That's what happened to me. It was my Festiva Maxima and only a lobe of a leaf was infected. I would snip that off and next week another lobe would be infected. I kept cutting bits of it off every week. Then it stopped. I was happy about that because it's a small plant! Luckily, the single bud made it and is blooming :) Then it showed on a couple of other peonies to a lesser extent except for one where one shoot with bud died. (Yes, cut it off.) I intend to use that bordeaux mix or crushed limestone for next year.