Fill a box or flower pot with peat moss. Water the peat until it's evenly moist but not wet. The peat may need 30 minutes to fully hydrate if it's dry. Drain out any excess water before storing.
Bury the peony roots in the moistened peat moss. Arrange the roots so they aren't touching each other.
Place the roots in a cool storage location, such as an unheated garage or basement, until you are ready to plant. Monitor the moisture in the peat and water it before it dries out completely. Peony roots can usually store for up to two weeks without any root damage.
Examine the roots after storage and before planting. Soak any roots that have become dry and wrinkled in a bowl of lukewarm water for two to three hours before you plant them.
Plant the peony roots with their tops, where the buds are located, sitting 2 inches beneath the soil surface. Space the roots 2 feet apart. Water thoroughly after planting.