According to the Royal Horticultural Society website -
Propagation

* Take semi-ripe cuttings in summer or graft in winter.
* Sow seed in containers outdoors in autumn or early winter. They may take three years to germinate.

They didn't seem to keen on the effectiveness of air layering.

Margaret

I have read that this does seem to work in Tree Peonies but I have yet to try it.I have many books on peonies and I know that it has been successful but don't remember which book I read it in.It may have been The Best of 75 years avaliabe through the American Peony Society.

Air layering used to be quite common for many plants including tree peonies. Like all things the cycle of interest has spun again and people are trying air layering again. Make a couple of nicks in the skin where you are attempting to air layer, let dry, then apply which ever method you are using to the cut area of the branch.