I have a friend who has Giant Bird of Paradise that doesn't get a lick of sunlight and it does great! Obviously this would be too tall for your carport. Perhaps a regular Bird of Paradise would do equally as well.

Plumeria would work, but would have to be brought in before the temps reach 40 at night.

My Dwarf Banana Tree is indoors now - but used to be outside in full shade and did fine. I am not sure how they handle the cold though being a tropical plant.

As for annuals - My Dwarf Sunflowers do well in full shade.

I have a couple of spider plants that I have in pots outside all year long. In the winter I let them get a little sun but in the summer they do better in total shade.

Here is a link that might be useful: {{gwi:412014}}