The best time to transplant peonies is late summer, or even very early fall (late August -early Sept). The trick will be to keep them well watered and protected from too much heat and sun until they can be replanted into garden soil in your new location. I think if it were me, I would dig the clumps with as much soil as possible, and pot them up in large containers with good drainage holes; keep them out of strong sunlight and wind, and make sure they are well watered, regularly. Then when you plant them in your new location, choose a spot that is sunny and well drained and don't re-plant them too deep. If you divide the clumps, be sure that each clump has at least 3-5 eyes(buds). Please note: you should not move plant material across state lines unless it has been inspected and cetified as pest free by your local State Dept. of Agriculture Inspecter. This is very important so that insect and disease problems are not inadvertantly spread around our country.
