From the ArcaMax Publishing, Gardening Newsletter:
http://www.arcamax.com/news/gardening/s-1894-312700
Question: I have the most beautiful peonies! Every year I carefully
disbud them to make the rmaining flowers larger--but then the flowers
get too heavy and fall over. Is there anything I can do to make the
stems stronger?
Answer: As you've seen, disbudding, or removing all but one flower per
stem, results in fabulously large flowers! However, even if you didn't
disbud, chances are you'd have problems with the plants toppling over
under the weight of the flowers. However, overfertilizing can
contribute to overly succulent, and therefore weak, growth.
There are several methods of supporting the flowers. Whichever means
you select, it is a good idea to set it up before the peonies reach
their full height. One is to use the purpose-built traditional peony
rings which are short enough to "disappear" as the plants grow up
through them and broad enough to encompass the entire plant.
Another method is to set several stakes in a ring around the perimeter
of the plant and then wrap string spider web style around and through
the stakes; again the plant will grow up and through the support.
Yet another method is to set a section of wire mesh such as chicken
wire on the ground and allow the plants to grow up through that,
raising it with them as they grow taller.
These will all support the plants evenly and gently and be nearly
invisible. Finally, if all else fails or it is too late for the early
support methods, simply tie a few lengths of string around the
perimeter of the plant. This will enable it to hold itself up...but
also makes it look like a trussed chicken.
Enjoy your peonies!