I stored some this spring for a couple of weeks. Here's some info:

Here is a link that might be useful: Storing Peony Buds

I found a link online, unfortunately don't remember where, where they mentioned you could do this for up to 6 months. They said to cut the stems when the buds were in marshmallow stage, not too hard, not too open, and store them in the fridge for up to 6 months. I bought some at a boutique market about a month after all our local ones stopped and they literally started opening within an hour after cutting their stems and putting them in water and were fully open a day later so I wondered if they had been 'delayed' that way.

wish I'd had hands on experience but so far, just read about it!

This is not the link I found but has similar info.
http://www.deeprootsathome.com/store-and-keep-peony-buds-for-weeks/

Thank you very much for those ideas, Moissy and Portia. I will try those next year and hopefully delight my sister with peonies when she visits.