From AN INTRODUCTION TO HARVESTING AND SELLING CUT FLOWER PEONIES....
https://uaf.edu/files/snre/MP_...
All flowers at the GBG were harvested at the "marshmallow" stage which refers to the firmness of the flower bud at harvest. When holding the stem at the base of the bud between the index and middle fingers and pressing down on the top of the bud with the thumb, the bud has about the firmness of a stale marshmallow. No solid spots can be felt in the core of the bud. At the GBG, Jan Hanscom and I chose this method for its simplicity and because of our lack of experience harvesting flowers.
The same document has a numeric table for stages of bud development.
1.0 Hard tight bud, little petal color
1.5 Hard tight bud, slight color
2.0 Firm tight bud, petals showing color
2.5 Slightly softer bud, "squeezable" (Marshmallow stage)
3.0 Loose or soft bud. Outer petal loosening, petals still firm
4.0 Very loose bud, "hollow feel"
5.0 Almost out, petals curved inward
6.0 Open (optimum) petals reflexed
7.0 Petals reflexed and wilted or dropping
Quite a few cultivars were safe to harvest at stage 1.5 or 2.0 and would enjoy a longer storage life when harvested so early. Pink Hawaiian Coral, Coral Sunset and Festiva Maxima were all harvestable at 1.5 and Sarah Bernhardt was listed as a 2.0. The chart is very limited and so experimentation with your own flowers will be necessary.