I found this article in the Fine Gardening Magazine. What a great way to enjoy your peonies longer.
HOW TO MAKE PEONY BLOOMS LAST LONGER
Because peonies blossom all at once and so early in the season, try extending their bloom time with cold, dry storage. When the first crack of color appears on the hard green bud, cut the stem (to about 16 inches long), strip off most of the leaves, and wrap as many as 10 stems in three layers of tissue paper.
On the outside of the tissue, mark the date and pop them in the refrigerator. For up to three weeks, you can pull the stems out of the fridge, cut an inch off the bottom of the stem, and stand them in fresh water to rehydrate.
In just two days, the stems will be in full bloom.