Team Logo. The Charleston Rainbows were a team in the South Atlantic League. They were the Low-A affiliate of the San Diego Padres. In 1994 they changed their name to the Charleston RiverDogs. CharlestonRainbows.com Retrieved from "https://prosportsteams.fandom.com/wiki/Charleston_Rainbows?oldid=17328" Categories: Former SAL Teams Teams in South Carolina Add category Cancel Save Community content is available under CC-BY-SA unless otherwise noted.