If you absolutely need to move it now you can, certainly never preferred to move any perennial right in the middle of it's short active growth cycle. If you have to move it dig up as much soil around it as possible to avoid damaging the roots or exposing them to air. Water them enough so that they don't dry out before being replanted but don't leave them boggy. Store them in enough shade that the roots don't overheat in whatever temporary container you have them in and treat them as a tender perennial when they're replanted. Provide several weeks of shade during the hottest part of your day once they're in their new home (put a lawn chair over them or umbrella, anything temporary) and keep them from drying out, again they don't like boggy situations so don't overdo it.

My father tried moving a peony in June, and in his mild climate it just died.

There is an ideal time for transplanting just about anything and then there is the time at hand :-) If you are careful and follow the instructions provided by lizbest1, you can do so now.

I've done it before successfully, certainly is doable but no where near optimal time to move them. The only time I've done it is when they'd be killed left where they were when hardscape had to be put in.

Thanks for the advice... I'll wait til the fall... was trying to get a head start cleaning out the area where they sit now, but I can do it next year.