Peonies don't like to be moved, they may need a few years to settle in. You'll probably get a few flowers next spring :-)

How long ago did you move them? It's not unusual for them to miss a year of blooming after a move. Also, peonies planted too deep won't bloom. The eyes should be only an inch or two under the soil. Hope the bloom for ya next year!

Just plant them in a good organic soil, with bone meal, compost, well-rotted manure beneath root and in full sun area. The eyes should not be more than 1-2 inched below soil. Should also have good drainage, shy away from synthetic fertilizers or too much water. If the root is more than 3 years of age and is too large, you may want to divide it in its dormant stage. Fall planting and transplanting is recommended. (after 1st week of September). Good luck!