Honestly, the best time to transplant peonies is in September. However, you may successfully transplant peonies in the spring, though you should be aware that plants moved during this season are not likely to produce the abundant flowers or foliage they've produced in the past---or may take a season or two before they start blooming.
Remember that peonies need direct sunlight, so observe the new location you've chosen to make sure it receives at least six hours of sunlight per day.
Cut the peony stems to ground level prior to digging up the plant.
Place the edge of your shovel at the edge of the root base, and firmly press down to break apart the soil.
Lift the plant out of its current space gently, so as not to break any roots. Shake off excess dirt to expose the root system to the air.
Prepare the location where you wish to transplant the peony and dig a hole large enough to accommodate the root system, and deep enough to allow for layers of compost and fertilizer underneath the soil that will surround the roots.
Place the plant in the prepared hole, so that the eyes on the roots are only one to two inches below the surface. Cover your peony with mulch and soil to protect the newly transplanted plant. Water it heartily.