Rivina humilis is considered invasive in some places but I think that in Austin it is a reasonably well behaved ground cover plant. Most of the sources I read said the plant is easy to grow from seed and widely dispersed by birds yet I couldn’t pin down some details. One place summed the situation up like this:
I guess I will just collect some seeds and wing it.
When to sow: In the spring after the last frost.
Special treatment: Collect berries when red and perhaps overripe. Clean and dry the seeds. They can be stored.
Fresh or dried seed: Dried
Planting depth: ?
Preferred temperature for germination: ?
Days to germination: ?
Vegetative propagation: Stem cuttings in spring.