I found info below on Wikipedia. I think they mean King’s Island in Cincinnati since there’s no Coney Island there.
“For the first season, some of the live-action segments, specifically those used during the musical segments, were shot at Six Flags Over Texas. For the second season, filming took place at the Coney Island amusement park in Cincinnati, Ohio. In many episodes, the Banana Splits were seen riding the many rides at Six Flags and Coney Island.”
