Can the Chinese tree peony be raised in pots? If so, what should be done in order to make it grow and bloom?

Yes, they can be raised in pots. It requires knowledge and very careful cultivation.
The plants have to be the low growing, upright, strong, free blooming varieties with many feeding roots. Hu抯 Red, Silver Red, Beautiful Spring Red, Champion Pink, Big Brown Purple, Zhao抯 Pink, Lantian Jade, White Jade, Cinnabar Rampart, Purple Velvet, Shandong Pink, Number Eighteen, Sunrise Red and Champion of Black Flowers, Twin Beauty, Luoyang Red, Cao Zhou Red are the varieties good for pot planting.
The potting soil must be loamy and rich. Use clay pots at least 10 inches in diameter with 10 inches depth. Transplant it to larger pots as the plant grows. A pot with the same diameter from top to bottom is a better choice.
The fall is the best time for potting the tree peonies. After digging up a plant leave it out for a day or two to let it become limp for easy handling. Remove damaged branches and some of the branches which are very closely grown together. Cut short the very long roots to fit the depth of the pot. Soak the pot in water thoroughly. Put the plant in and fill the pot with soil not all the way up to the brim, firm the soil and water it well. Do not over water, just keep it moist, not soggy. Use organic fertilizers with water twice a month during its growing season. Once a week right before blooming and during its blooming period. Afterwards resume the once or twice monthly routine.
In places where the winter is severe the pot can be buried in the ground with the plant exposed outside, then cover it or leave it according to the local climatic condition.