[3] After a two-season stint in the Philadelphia Phillies' minor league system with the Klamath Falls Gems, Miami Eagles, and Salina Blue Jays,[5] Convy began his career in the entertainment business as a featured performer and singer in the Billy Barnes Revues of the 1950s and 1960s.

Convy went on to become a Broadway actor, starring as Perchik in the original cast of Fiddler on the Roof (1964), appearing in The Impossible Years (1965), and creating the role of Cliff Bradshaw in Cabaret (1966).

[6] In 1979, he appeared on Password Plus with fellow celebrity contestants such as Elizabeth Montgomery, Carol Burnett, Phyllis Diller, Judy Norton Taylor, Marcia Wallace, and Elaine Joyce.

Their first production was a game show titled Win, Lose, or Draw, which made its debut in 1987 as part of the NBC daytime lineup and in nightly syndication.

Convy turned to acting full-time in 1956 and was in the musical The Billy Barnes Revue in Los Angeles before moving to New York City.

In the 1960–1961 season, Convy guest-starred on Pat O'Brien's short-lived sitcom Harrigan and Son and the series 77 Sunset Strip in the role of David.

In 1974, Convy portrayed Lieutenant Steve Ostrowski, the police officer nephew of elderly amateur sleuths on the short-lived series The Snoop Sisters.

Throughout his career, Convy was a frequent guest star on series such as Bewitched, Hawaii Five-O, The Partridge Family, Mission: Impossible, The Silent Force, The New Phil Silvers Show, Fantasy Island, Charlie's Angels, and Murder, She Wrote (including the pilot episode).

On The Love Boat, Season 2 Episode 11: "Legal Eagles" (1978), he played Danny Holt, a divorced man who falls for his ex-wife's lawyer.

Convy had joined the project when it was recast after its intended premiere in the 1982–83 season was delayed; he earned the role originally given to Larry Breeding, who was killed in a car accident in September 1982 after the first pilot had been shot.

His other film credits included A Bucket of Blood (1959), Susan Slade (1961), Philippe de Broca's Les Caprices de Marie (1970), SST: Death Flight (1977), the horror film Jennifer (1978), Hanging by a Thread (1979), Racquet (1979), The Man in the Santa Claus Suit (1979), Hero at Large (1980), The Cannonball Run (1981), and the television movie Help Wanted: Male (1982).