Asclepias incarnata would look very nice behind your coreopsis. It blooms all summer and loves heat. Cannas would too. In front of your coreopsis, it would be hard to beat daylilies in any of a thousand shades of red,orange, or yellow. You could also add some chrysanthemums for late summer and fall interest. Rozanne geraniums would add some nice color contrast with her blue blooms all summer long along the front edge. All of these would tolerant some shade and do well in high heat.

If you want to add some annuals, you could use Profusion Zinnias. The Fire one is very nice. Also Salvia, Victoria, would be nice with your hot color palette. It gets about 18 inches and blooms all summer long: bullet proof in Mississippi heat, and will tolerant a bit of shade too.

How tall are your Coreopsis? I have some like 'Creme Brule' that are less than 18" tall, and then I have Coreopsis grandiflora 'Sunburst' which easily gets 30" - 36" tall. My entire garden is in the colors you are looking for, so here is some of what I have planted with my Coreopsis:

Achillea 'Paprika'
Achillea 'Terra Cotta'
Achillea 'Walter Funke'
Achillea 'Anthea' (pale yellow)

Echinacea 'Harvest Moon'
Echinacea 'Sunrise'
Echinacea 'Sundown'

Gaillardia 'Goblin' (looks great next to Coreopsis 'Creme Brule')
Gaillardia 'Oranges & Lemons'

Geum 'Blazing Sunset'
Geum 'Fireball'
Geum 'Mango Lasi'

Lychnis 'Lumina Bronzeleaf Red' (smaller version of Maltese Cross)

Penstemon pinifolius 'Compactum'
Penstemon barbatus 'Coccineus'

... plus several red and yellow daylillies, mums, and sedums.

My garden is in full sun, and I'm in a high dessert climate, so any of these would do well in your sunny spot, as long as it doesn't get too wet there. Can't help you with the shady side, since I don't have any here.

Hope this wasn't "too much information" : )

Bonnie

It might not be what you are thinking of, but what about an ornamental grass, perhaps like prairie dropseed, which changes colors in the fall (from green to yellow/orange)?

The link below has a description and a photo of it paired with asters.

Here is a link that might be useful: Prairie dropseed

Thanks for all the suggestions. I think the sunny spot is going to be overwhelming in its choices. But that darn spot under the tree....argh!

What kind of tree is it? If it's a maple, it's difficult to grow under any of them. They have profuse surface roots that suck the moisture out of the ground. You also need to be careful because some trees are sensitive to root disturbance.

Under the Sugar maple near the garden, I don't have much, because Sugar maples have sensitive roots, but put a few thing that can hold it's own under a tree. Daylilies, some bulbs, some False Solomon's seal.

Hostas are often planted under trees.

For shade,

gold leaved hostas
zig zag goldenrod
varigated hakone grass
Goldstrum rudbeckia
there is a yellow toadlily, can't remember the species
red astilbes (most are really dark pink though)
yellow meadow rue (thalictrum)
I'd try daylilies too.

Ted

What about gallardia? There are also the red and orange cockscombs, pentesemon-husker red,marigolds, geraniums,nasties. I think you have alot of options here.
Good luck.

There are a bunch of local plant sales coming up, so I'm going to take this list with me and see what kind of damage I can do to my wallet! Thanks!