Answer: If the plant is setting flower buds that fail to open, there may be a problem with late spring frost damage due to the microclimate at the new planting site. Covering the plant if a late frost threatens might help. If it is growing buds that discolor or turn gray/fuzzy, then there may be a problem with a fungal infection such as botrytis. Be sure to clean up sall the peony stems and foliage in the late fall and dispose of it in the trash to try to limit reinfection.
If the plant does not seem to be developing flower buds, there are several possible causes. One would be it needs more direct sun -- they do best in full sun all day or at least a half a day of full sun. Or, it may have been replanted too deeply. The eyes should be about two inches below the soil surface. Sometimes the plant will settle lower after planting and this will prevent flowering. Finally, transplanting peonies causes them stress and they often refuse to bloom for two years or so after the move.
I hope this helps you trouble shoot.
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