Peonies in Florida
Peonies require a long cold spell for their winter dormancy, with temperatures 40°F or below. Gardeners have gone to great lengths to "trick" the plants into thinking they are growing in a northern climate, including dumping bags of ice on the crowns of the plants. It's a lot of work and isn't very successful. It's better to grow selections that are more suited to your climate.
There are some varieties that will do well in Zone 8, and some gardeners have had luck with them in Zone 9. Look for 'Festiva Maxima', 'Kansas', 'Pink Hawaiian', 'Doreen', 'Raspberry Sundae', and 'Sarah Bernhardt'. Provide the coolest conditions that you can by planting on the north side of your house, as long as the plants are still getting at least half a day of sun.
You may have more success with tree peonies. Their woody stems do not go dormant. There are a number of varieties that are recommended for warmer climates. Check with local nurseries, or for specialty nurseries on the Internet, such as Cricket Hill Gardens.