* "Into the Woods" (1987) by Stephen Sondheim features Cinderella as a main character, but it's not a full-fledged Cinderella musical.
* "Rodgers & Hammerstein's Cinderella" (1957), a television musical, was composed by Richard Rodgers with lyrics by Oscar Hammerstein II. It was later adapted for the stage in 2013.
So, depending on which version you're asking about, the composers are either Stephen Sondheim or Richard Rodgers and Oscar Hammerstein II.