Starting to show up on the internet.
But in ignorance, I planted the common varieties from Home Depot and they have been blooming well for four years. Some neighbors have decades old patches of peonies-nothing fancy, but beautiful for a time. )And I've seen the tree peonies in bloom at the Kentucky arboreteum in Lexington.

Here is a link that might be useful: more pictures than my land line can load

That was my piece on VG. The Auburn project is trialing tree peonies (Paeonia suffruticosa) in the deep south. Herbaceous peonies, which it sounds like you're craving, are a different complex of species and hybrids. But good news -- you can grow those big old fashioned types you long for here in the south. The trick is to pick the right varieties. In general, go for early blooming types. The later the bloom period, the less successfully that cultivar does in our heat. Some of the oldest and most tried-and-true cvs are quite happy in our climate. Here's what's done well for me:

Festiva Maxima (white)
Bowl of Beauty (Jap with rose pink petals, creamy yellow staminodes)
Red Charm (a wonderful true red, but be prepared to pay through the nose)
Kansas (rosy red double, very reliable)
Shirley Temple (blush daughter of Festiva Maxima)
Paula Fay (bright pink semi double)
Mons. Jules Elie (light pink)

All the above are more or less fragrant. Festiva Maxima and Shirley Temple are intensely fragrant.

I haven't grown them, but a friend near me has Coral Charm and a yellow (I believe it's an intersectional peony, a tree-herbaceous cross) that both do great. The yellow one costs dearly, but it's spectacular.

Marty

Thank you, both, for answering! I am so excited that it is truely possible to have these grand flowers here. After 10 years in Texas, I doubted I'd ever have peonies again. I'm finding more and more that the climate here in Tennessee is going to let me "push the zone" on either side.
While I don't post here much, I do check out the forum at least a couple times a week and I'm so glad y'all are here.
Thanks, again,
Linda