Ask Mr. Smarty Plants

It sounds like what you would like to have is a meadow garden, but you don't really have the right plants for it. Bermudagrass, as you will see from this University of California Integrated Pest Management website, is native to Africa and is one of the most invasive weeds in the South and Southwest. Besides the fact that it would probably climb over and choke most flowering plants that would grow there, it needs a lot of sunlight, and growing around trees is not going to work. The next thing we want to talk to you about is oleander. From a previous Mr. Smarty Plants answer:

"This article from Floridata will give you some information on Nerium oleander. Please be sure to read the Toxic warning at the bottom of the page. All parts of this plant are toxic, and it is not even safe to burn it, as the smoke retains the toxicity. It is native to North Africa. For more information on the toxicity, read this Howstuffworks.com article on The Top 5 Most Poisonous Plants."

So, we suggest you scratch the oleander. On to the canna lilies. There are two members of the genus Canna native to North America: Canna flaccida (Bandanna of the everglades) and Canna glauca (Water canna). Both of these plants require quite a bit of sun and wet or moist soil, such as freshwater marshes and swamp margins, which doesn't sound much like Tarrant County. Neither is shown by the USDA to be growing natively anywhere near where you are gardening. 

Most of the cannas in cultivation and commercial trade are hybrids of tropical plants native to Mexico, Central and South America. These have an all-inclusive name of Canna x generalis.  Here is an article from Floridata Canna x generalis with more information. Since the Lady Bird Johnson Wildflower Center is dedicated to the growth, propagation and protection of plants native not only to North America but to the area in which the plants are being grown, none of these are probably ideal for your situation.

We would suggest that you rethink your garden plans. With a rocky bermudagrass area under trees, it is going to be difficult to find anything that will flourish without substantial alteration of the area. Although you feel it would be impractical to have raised beds, we still feel that they would be best for your garden, along with eliminating or, at least, controlling the bermudagrass, keeping it out of the raised beds. You could then plant shade tolerant plants and achieve the added color you are looking for. Nothing planted directly in the grass is going to thrive. Another possibility would be large pots with blooming native plants in them; either perennials or annuals that can be changed out from time to time.

If you go to our Recommended Species section and click on North Central Texas on the map, you will be able to get some plant lists for herbaceous blooming plants. On the sidebar on the right side of that page, you can select on "Herb" (herbaceous blooming plants) under General Appearance, "Part Sun" ( 2 to 6 hours of sun daily) under Light Requirements, and "Dry" under Soil Moisture, and then click on NARROW YOUR SEARCH. When we did this, we got a list of 21 plants that should do well in the conditions you describe. Follow each plant link to our page on that particular plant to find out when and what color it blooms, what its Growing Conditions are and Propagation Instructions.