Are these in the original pots that they came in or did you transplant them over to new pots? It is best to keep them in the original pots that they came in to avoid disturbing the roots. Any disturbance to the roots while they are growing, budding, blooming will affect the plants' flower bud developments and flowering. They will recover. Keep them in a cool spot, with filter partial shade is best. You can plant them in late August or early Sept.

disbudding is an idea worth considering to preserve their strength

Will you be keeping them potted? What growing zone are you in? Make sure your pots have plenty of drainage. Use a potting soil that has pieces of pine bark in it to aid in drainage. Peonies don't want wet soggy feet. Have they perked up since you posted your pictures? When you cut off the dead bud make sure you dispose of it. Peony trimmings should not be composted or kept near the growing plants.