Peonies have very large tap roots and they wouldn't last too many years in pots, even really large ones. It could be a temporary holding bed for them, but unless they're at least 2-3 ft tall, they won't do well or flower.
And yes, they can be prima donnas for their needs.
The only problem with planting another one in a previous peony spot, is that you might not have removed every bit of old root, which could mean the old plant will grow again and interfere with the new plant. Perhaps you can trade a friend for a plant.