The reduction in the number of peony flowers could be the result of a number of factors.

• Buds killed by a late Spring frost, fungal disease, or thrips, for thrips spray with a pesticide labeled for use on peonies. Make sure to read and follow all the label directions on the pesticide.
• Peonies are planted close to trees or shrubs. The tree or shrub roots are starving the peony roots for nourishment.
• The peony is planted too deep. Replant with the eye of the peony two inches below the soil line.
• Not enough moisture in the ground. Water the peony deeply.
• The peony is immature, wait for the plant to grow several more years.
• Excessive hot weather.

The following article provides more information on peonies: Peonies for the Home Landscape | NC State Extension Publications (ncsu.edu)