No, no, no - there are very few plants that work under a maple. The only thing I get to grow there is ivy!!! In fact, if I had the money, I would remove my maple because I now trip over the roots that have taken over my yard!!!
Peonies need sun to bloom well. They should be planted in the fall (ideally) but I can't find them then locally. You can order them in fall from peony sellers - online or wherever.
I have bought them in the spring (blooming in pots) and planted and they are fine. Last year I bought roots from Sam's Club & Walmart, planted them in potting soil in large pots. The roots have little reddish buds on them which should be only 1-2 inches below the soil. I let them grow all summer (taking care to keep them watered) and planted them in the fall. They are doing well, some have a few blooms this spring. This saved me a bunch of money because I wanted quite a few.
The roots eventually go very deep (2 Ft.) so I prepare the soil well to that depth. My yard has boodles of rocks so I have to excavate so the roots can grow!

I'm afraid I have to agree -- there's no point to planting a peony under a silver maple. Peonies like a lot of sun, and they won't get enough water or nutrients under a big greedy maple. Not to mention the rough time you'll have digging a hole big enough through all those roots! I would wait until fall to plant, too. Gilbert H. Wild (online website) sells bare-root peonies for fall shipment, for a good bit less than the potted plants cost in my area at garden centers.

Thanks for your replies sue and jayco. I guess I won't plant one there, then. I guess I had gotten the impression that they do well in shade. There's no point in buying and planting if it's just going to die or barely live and not bloom nicely.

Thanks again.