Vine with red berries
I found a native vine 2-3 years ago with bright red berries, sort of translucent red, and shiny. I cleaned up the fruits and each one had a single unique seed. So, it was easy to identify the vine as Moonseed Vine, or Carolina Moonseed Vine--even though it grows wild in the greather Houston area.
I put the seeds out in the top 1/4 or 1/2 inch of good potting soil, in a gallon container and left them over winter--exposed to the rain and sun. The seeds germinated in spring and after the tops were a few inches high I put them up into individual containers for another year. Then, I planted them out.
The vine is not exactly slow growing, but it is a well behaved vine--not at all rampant. It will grow to the top of a small tree (plum tree) or over some shrubs and is mostly not noticeable until the berries ripen. Then it is very attractive.
The link below can guide you to a seed source so you can grow your own vines.
Here is a link that might be useful: Botanic Garden Vine Article