Conway’s early film credits include the cult horror films I Was a Teenage Frankenstein (1957) as the monster, How to Make a Monster (1958) and The Saga of the Viking Women and Their Voyage to the Waters of the Great Sea Serpent (1958). In 1958, he was cast in the “Man Hunt” episode of the western aviation television series, Sky King, with Kirby Grant, Richard Beymer and Gloria Winters.

In 1960 Conway appeared as Orderly on the TV western Maverick in the episode titled “Thunder from the North.” In 1960, Conway appeared as Lt. Charles Williams in the episode “Absent Without Leave” of the ABC/Warner Brothers western series, Colt .45, starring Wayde Preston. Tyler McVey was in the guest cast as Col. Ben Williams, and Steve Brodie also appeared in the episode. He also appeared in 1960 in three episodes under the names of different characters on the ABC/WB crime drama, Bourbon Street Beat, starring Andrew Duggan. In 1966 Conway made an unsuccessful television pilot Assault!, made by the producers of Combat! about the US Marine Corps in the Pacific in 1942.

Conway starred with Bette Davis in the 1972 television movie The Judge and Jake Wyler. In 1973, Conway was featured in Playgirl magazine’s August issue. He also guest-starred as the murder victim in the 1973 Columbo episode “Any Old Port in a Storm”.

Conway and his Burke’s Law co-star Gene Barry remained close friends until Barry’s death in late 2009.