The best time to move peonies is in the fall. I have never lost a peony that I have moved during the spring and summer but they certainly have not thanked me with blooms the following year. In fact whenever I move peonies anytime other than fall, I am guaranteed to lose the blooms for the following year. The only time that this does not happen, is when I do the moving in the fall.
I suggest planting the eyes of the peony just slightly below soil level, approximately 1 & 1/2″ below the soil. Add some compost to your planting hole. It is okay to cut the foliage down at this time also if it is looking a little rough. This is also an ideal time to divide peonies if that is needed.
Good luck with moving your peonies and let’s hope that the fall move still allows those beautiful early summer blooms.