Coco is one of two (the other is Amy Irving) actors (as of 2005) to be nominated for both an Oscar and a Razzie Award for the same performance: As Marsha Mason's gay best friend in Only When I Laugh (1981), Coco got nods for both Best and Worst Supporting Actor. He did not win either award.
He studied drama at HB Studio in Greenwich Village in New York City.
Lived for quite some time in his Greenwich apartment near friends playwrights Terrence McNally Paddy Chayefsky and Israel Horovitz, and actor Robert Drivas, where they all would often get together for a weekly game of poker.
Resuming press interviews in connection with a Diet Coke commercial he filmed in 1986 (after being out of work for a while), he said he was proud of having lost 42 pounds for the job.
Though he never married, he had what he later described to a People Weekly magazine interviewer as a passionate romance with stand-up comic Rusty Warren. Although she did not leave behind any known television or movie credits, she is fondly remembered as the "Knockers Up Gal" by those who bought her comedy albums in the 1960s.
Was nominated for Broadway's 1970 Tony Award as Best Actor (Dramatic) for "Last of the Red Hot Lovers."