Annual fertilization of peonies works well when applied in two treatments. One should be applied before the leafy shoots commence growth in early spring and again right after flowering season has run its course. The early application can be applied any time from autumn until early spring. The amount to apply at one time will vary with the size of the plant and whether the planting site is already quite fertile soil. The amount somewhere between a fistful and a quarter cup.
For a granular dry fertilizer, select a formulation made in a 1-1-1 ratio of nitrogen-phosphate-potash, which might be up or down from a 10-10-10 (percentages). Apply the product in a thin ring around the clump about 6-8 inches out from where the stems will come out of the ground. The benefit of the supplementation is quicker if the fertilizer is cultivated in and watered.
For additional information on peony growth needs, we recommend you study the article Growing Fine Peonies.