Ask Mr. Smarty Plants

Those are tough conditions with the only sun the plants get being the hot late afternoon sun.  You are going to need a plant that will tolerate part shade (2 to 6 hours of sun per day) and heat.  The fact that you will be growing these in containers rather than the ground is going to make it more difficult.  Plants in a container can become overheated in the hot sun; whereas, plants in the ground will have the heat dissipated better than in a small container.  We have an article, Container Gardening with Native Plants, that you should read.  You should also read the answer to a recent question dealing with plants grown in containers and suffering from the heat. 

Now for the plants—you didn't say but I imagine you would like an evergreen.  Here are a few evergreens that should work:

Morella cerifera (Wax myrtle) will grow in sun and part shade 6 to 12 feet high.  There are dwarf varieties.

Ilex vomitoria (Yaupon) will grow in sun, part shade and shade 12 to 25 feet high. There are dwarf and columnar varieties and they can be pruned.

Prunus caroliniana (Cherry laurel) is a small tree that will grow in partial shade to over 20 feet, but could be maintained in a container for several years before growing too large.  Here are more photos and information.

Yucca arkansana (Arkansas yucca) grows in part shade and, with the flower stalk, can be 6 feet high.  Here are more photos and information.

Sabal minor (Dwarf palmetto) grows in sun, part shade and shade 5 to 10 feet tall and can grow to be 4 feet wide.  Here are more photos and information.