Okay, I take it the bed is at the very back of the carport. I'm trying to picture how the house blocks it on three sides, but anyways you say it gets no "direct sun". Is it pitch black at the bed or does it get some light? Light bounces around (off houses, concrete, the ground, etc).

I know I am WAY out of your zone, but I did grow up in OK so I do know the climate (plus I love watching Paul James on HGTV). :) One thing I have picked up from him is that a lot of plants/shrubs that we consider hardy and sun-loving aren't even supposed to grow in your area but he grows them protected under the canopy of his trees.

I just ran quickly through one nursery suppliers catalog and these are some of the shrubs that can take full shade:
1. Taxus (Yew) - comes in all shapes and sizes.
2. Stephandra incisa 'Crispa' - Cutleaf Stephandra is a graceful, low spreading plant. Miniature maple-like leaves unfold a reddish -bronze, small white flowers in late May. 2-4' (I love the look of this plant).
3. Rhamnus frangula 'Ron Williams' - "Fine Line" - narrow column, fernlike foliage, non-invasive.
4. Rhodotypos scandens - Black Jetbead - sngelic pure white flowers in June, glossy black, bead-like fruit remains attractive throughout the winter. Performs wonderfully in the shade. 3-6'
5. Ribes alpinum 'Green Jeans' or 'Green Mound' - glossy, rich green leaves and excellent branching, superior summer leaf retention. 3-4'
6. Itea virginica 'Sprich' - "Little Henry" - new, compact sweetspire, pur white flowers in early summer cover this low mounded, compact shrub, vibrant fall color even more than the burning bush. 24-36" by 3' wide.
7. Kerria japonica - (Japanese Kerria) - many varieties, white or yellow flowers (single and double), colorful green stems for winter interest, sizes range from 3' to 5'
8. Euonymus fortunei - many varieties - cream & green leaves or gold & green - mounding, spreading, or climbing types - sizes range from 18" to 3'. (great splash of color for a shady spot... and evergreen).
9. Diervilla lonicera 'Copper' - Bush Honeysuckle - copper-red new growth, yellow flowers mid-summer, great for dry sites. 2'-3'
10. Diervilla sesslifolia 'Butterfly'- rich yellow flowers held in upright clusters from May to July, foliage is bright green and clean, well-branched, never floppy like other culivars, adaptable to dry shady locations. 3'-5'
11. Buxus microphylla 'Faulkner' - glossy foliage, one of the very best boxwood for milder climates. 2-3' (all the Boxwood listed as full sun to full shade).
12. Azaleas and Rhododendrons - both like being under trees in hotter climates and there are tons of varieties and sizes.

That is just a few of the shrubs for shade. Paul James has many of the dwarf evergreens that wouldn't normally survive your heat and he plants them under his trees. I believe he also has some varieties of Japanese Maple in the shade.

Perennials:
1. Heuchera Palace Purple
2. Hosta
3. Lamium (groundcover)
4. Japanese Painted Fern (actually most ferns)
5. Heucherella Sunspot
6. Athyrium Silver Falls
7. Brunnera Jack Frost
8. Tiarella - very tolerant of heat, drought, humidity and poor soil. Great color for shade.
9. Gaultheria procumbens (Creeping Wintergreen)
10. Caladiums - full to part shade - many colors & sizes.
11. Cornus canadensis - Bunchberry - miniature dogwood
z2-7 showy white flowers in late spring, scarlet berries in summer and whorled leaves that blush crimson in fall, plant in shade. 10"T by 24"W
12. Tricyrtis - Toad Lily - several varieties, shade-loving, Orchid-like blooms in fall.
13. Heleborus - Lenten Rose - winter blooming.
14. Convallaria - Lily-of-the-Valley
15. Dicentra - Bleeding Hearts
16. Cardamine pratensis 'Flore Pleno' (beautiful)

Annuals:
1. Jungle Gold Impatiens (must have full shade)
2. Dragon Wing Begonias
3. Coleus (some need shade, some want full sun)

I have already made this long enough so if you go to the link below to plantbynumber.com and you will see some great ideas for annuals for shade. These are in containers but many can be put in the bed. Also, you can always tuck a pot/trough/barrel in a flower bed...on the ground or raised up on a pedestal...or use a tall urn...or some hanging baskets above the bed.

Anyways there are tons and tons of plants...but at least now you have a lot to look up and think about. Wayside Gardens has a lot of the plants listed and more. Their website is:
www.waysidegardens.com

Here is a link that might be useful: Beautiful Shade Containers

What about water? How does this area get water?

You can probably push to a zone warmer with all that protection!

Here's a page for the best full shade shrub:

http://www.missouriscenicrivers.com/shade-shrubs.html

Here is a link that might be useful: Best Full Shade Shrub (Bush)