Since they're among other perennials that bloom fine the only thing I can think of is maybe too deep? Don't know what zone you're in but the eyes should be no more than 2" deep in cold areas and only 1/2 to 1" deep in warmer zones. I'm sure from the other flowers you mentioned that they're in a sunny spot. Is there room around the roots? They don't like to be crowded. One other thing could be too much water. If the area stays very wet the peony roots will eventually rot. You should post some pictures of the area they're growing in as they come up and through the early summer, maybe someone can come up with an absolute answer.
Only other thing I could think of is how big were the pieces that your replanted? Typically after moving a 3-5 eye division or bigger will take 1-2 years to bloom again. If there were fewer or no eyes it can be a year or more longer.
