The best time to transplant peonies is in the late summer to autumn period, specifically from late summer when the leaves begin to change color until late autumn. This timing allows the plants to be transplanted while they are entering dormancy, which reduces stress and promotes successful re- establishment. Transplanting in the spring is generally not recommended because the young shoots can be easily damaged. In summary:

• Optimal transplanting time: Late summer to late autumn, especially from September to October.
• Avoid transplanting in spring to prevent damaging young shoots.
• When transplanting, cut back stems to about 4 to 6 inches, plant with rhizomes about 1½ to 2 inches below soil surface, and water well.
• Peonies often take a couple of years after transplanting to bloom again fully.

This applies to both perennial (herbaceous) and shrub peonies. Autumn transplanting also coincides with the natural die-back of peony foliage and setting of buds for the next spring. Therefore, to maximize success, transplant your peonies preferably in September or October when they're dormant and the leaves are changing color into fall.