If it's absolutely necessary you can transplant now, definitely not the best time to dig and move any perennial in the middle of its growing season but peonies are no more fussy than most. If you absolutely must move them just dig out as much soil around the roots as you can so that they never get exposed to air, get them in their new spot as quickly as possible, keep the roots moist after moving but not soaked and give them shade for several weeks after moving and probably again through the hottest part of your summer. I've had to do it before, sometimes lost the blooms for that spring, sometimes not, just depends on the plant and how the weather is that year.

Transplanted 5 last year around the same stage of growth, a few bloomed that year. I'm a firm believer in early transplanting rather then late, logic being that they have more time to establish before going dormant, and will be better off the following year. You're a bit late though.

Fastink the problem with that reasoning is that until August peonies do not send out the white hairlike roots that it will be using to feed itself.