it can be pot grown, but after a couple of years will stop flowering.

I Use John Innes no3, 3/4 and the rest multipurpose and then add some grit give it all a good mix, plant the tree peony a little deeper than the pot it is in which it will encourage its own roots to grow, at the moment it will be grafted on to rootstock (thick part of the root) but over time it will make its own roots.

Ceramic Malaysian pots are a good size but go for the largest and well crocked at the bottom of the pot so the water can drain away, much with gravel once potted up

I would also put a support in they can easily snap when young if the wind is strong.
To be honest they do better in the open ground in the garden , but a bit of TLC at this stage will make it a better plant .

Gg

As GG says they 'can' be grown in containers but aren't really happy… Copy and paste the link below to see what the RHS suggests

http://apps.rhs.org.uk/advicesearch/profile.aspx?pid=711

The height our large tree peony gets to I wouldn't want it in any container, too top heavy!