Select a planting location that receives full sun 4 to 5 hours a day and shade or partial shade the rest of the time. Make sure the site is well drained with no standing water.
Choose a day in the late fall, September through mid-October, to plant either bare-root or potted tree peonies. Soak containerized peonies with water and let them rest at least two hours, allowing the roots to loosen.
Dig a hole 18 to 24 inches deep and 2 feet across. Spread a 2-inch layer of compost in the hole and sprinkle with a ½ cup of bonemeal. Separate the roots of a potted peony by hand. Set it into the hole and fill with dirt, ensuring the base of the plant remains at the same level as it was in the pot. For bare-root plants, make sure the spot where the roots and branches join is at least 4 to 6 inches below the ground's surface.
Water newly planted tree peonies until the roots and surrounding ground are soaked. Water weekly or when the top inch of soil is dried, until the first heavy frost of fall. Begin watering again in the spring, allowing the top inch of soil to dry completely between each soaking.
Check tree peonies weekly for pests or disease. In areas where botrytis fungus is prevalent, spray with a fungicide when the shoots first emerge from the ground, again when they reach 1 foot high and again just before blooming. Spray the plants with insecticidal soap at the first appearance of ants or other pests, covering both the top and bottom of leaves and all the stems.
Feed tree peonies with a 5-10-5 formulation of commercial fertilizer after the flowers have died in the summer. Spread the fertilizer at least 6 inches from the tree peony's base so that it doesn't touch the plant's crown.
Prune tree peonies only to remove diseased branches or to shape the plant. New blossoms grow on branches that are more than a year old, so cutting the branches will reduce flowering.