The very heavy double peony blooms which need support to keep upright will catch a lot of rain and rot. If you can shake off the water after a rain you may be able to keep them from rotting. You could rig a umbrella to keep out the rain. Warm summer rain remaining in the flower will cause it to rot, period. Al

I can't be there to shake it off every time it rains (which it keeps doing non stop) and I have too many to cover to keep out rain.

Then don't worry about what you can not control. Almost everyone that has grown the full double peonies will tell you that when they bloom it always rains. Either enjoy what you can or grow less full peonies.

It sounds like you're talking about small, unopened buds, not open flowers, rotting. This is probably Botrytis, a fungus, as you have guessed. I don't think either chemical or organic pesticides will be real helpful. And I think the issue is not so much rain getting on them, as poor drainage and poor circulation around the plants. Try improving the drainage by adding compost, and if you can spread the plants further apart, that should help.

Nope, I'm talking about fully open flowers rotting. The buds are okay. The plants have good drainage and air circulation, although they probably will have to be divided this fall.