Brunette, with large eyes and a deadpan manner, Ms. Cooper excelled at comedy. It wasn't easy drawing focus away from Lauren Bacall, the star of the John Kander and Fred Ebb musical (which was based on the Tracy-Hepburn film of the same name), but Ms. Cooper managed to do it as Jan Donovon, the drab ex-wife of Sam Craig, the Tracy character. She stopped the show with her punchlines in "The Grass Is Always Greener," a duet with Bacall's character, Tess Harding, in which the two women envy the circumstances of one another's lives. Ms. Cooper stole the number, sending the audience into gales of laughter with her nasal refrain "What's so wonderful?" Ms. Cooper also won a Drama Desk Award for her work. She would later tour with Bacall in the show, and toured again, in 1984, this time with Barbara Eden. Born in New York City, Ms. Cooper's musical theatre chops stretched back to Mr. Wonderful in 1956, and included ensemble roles in the original production of West Side Story (as Rosalie), Gypsy (as Agnes, the leader of the Hollywood Blondes, which back up Louise) and I Can Get It for Your Wholesale. She replaced Jane Connell as Agnes Gooch in the original production of Mame and played a variety of roles in the Jule Styne-Betty Comden-Adolph Green-Arthur Laurents musical Hallelujah, Baby!

During the 1970s, Ms. Cooper appeared in Two by Two, On the Town and Ballroom. In the 1980s, she took roles in a few straight plays, including Neil Simon's The Odd Couple and Broadway Bound.