Two methods are suggested for peony seed germination.
1: the seeds can be directly planted in the garden. A peony seed needs at least on cycle of warm-cold-warm before it will germinate. You can expect a certain percentage of the seeds to germinate the following spring, but some seeds may take up to two years to emerge.
2: The seeds can be put into plastic bags with a little moist, but not wet, peat moss. The bag is sealed and then placed in a warm place. this moist warm environment will initiate the rootlet to form, but be aware, this can take upwards of three months. I use bags with a zip top, label them with the seed type and date, and then put them in a basket on top of the refrigerator.
Check the bags periodically over the next months and when a white rootlet forms allow it to grow to about 2-4 inches long. Transfer the roots as they germinate to another plastic bag with moist peat moss and put them inside the refrigerator for another 3-4 months. During this time you can check them for the emergence of a leaf, I have had them do this within the three month period, these I remove and plant in a pot with the seed just at ground level. they can then go into the light and when the ground is warm enough plant them out.