I had ivy as ground cover at my house in New Smyrna. It spreads fairly quickly, and it's easy to start from cuttings.

Perennial peanut ground cover immediately comes to mind . There are several varieties . One grows quickly and one grows slowly . This is a nitrogen fixing plant and needs no mowing .

Another is Ajuga reptans Bugleweed or Carpet Bugleweed .
This ground-hugging ground cover produces a profusion of dark green to bronze- or purple-colored leaves in a flat rosette, spreading fairly quickly by runners or stolons . Plant on 6 to 12-inch centers for quick establishment of a thick ground cover. Six-inch tall spikes of small blue flowers are produced in spring to early summer and are especially attractive when plants are massed together. There are selections with foliage variegated in green, white, red, yellow, and pink. USDA hardiness zones: 4 through 10A .

The Beach Sunflower is a spreading perennial that has attractive, small sunflower-like flower heads which are borne throughout the year. These showy flowers have 10 to 20, pale yellow rays that encircle a purplish-brown disk that is ½ to 1 inch wide. Different species of butterflies are attracted to these charming flowers.USDA hardiness zones: 8B through 10 . Planting month for zone 9: Apr; May; Jun; Jul; Aug . Native to Florida .

Gazania is a perennial grown as an annual that grows well in rock gardens or in other hot, dry areas. It forms a very low, ground-hugging ground cover, producing bright yellow, orange or red, daisy-like flowers. Flowers close at night and on very cloudy days. Plants grow 6 to 12-inches tall with blueish foliage. Do not plant in the partial shade. Full day sun is required for healthy plants. USDA hardiness zones: 8B through 11 . Planting month for zone 9: Mar; Apr; May; Sep; Oct .

Use Google Images to see what these selections look like full grown . All of this info came from the UF website - soultionsforyourlife.com . There are more choices of ground covers there .

I'm very happy with the dune sunflower as a groundcover. One small plant for $5 quickly spreads to 4'x4' then 6'x6'. No irrigation but I did mulch the starter plants which got almost no rainfall.

I tried creeping jasmine and it never grew, just sits there the same size it was planted. Probably wants some water and would do better with irrigation.

I've also tried perennial peanut and it didn't do well either, planted at the same time as dune sunflower.

Also consider lantana. Available as a 9-pack from Walmart for $8-9 so $1 per plant. Does very well and butterflies love it. Mine is yellow. I have the orange version too but it gets taller, about 2' tall.

I have mimosa (see link) and one small pot that I put out about a year ago covers about 25% of my front yard(it grew right on top of the mulch!).

http://www.allnativeflora.com/SunshineMimosa.htm

It has the cool 'lollipops', which I love.teeka