Canary was born in Elwood, Indiana, but grew up in Massillon, Ohio. He was the middle son of Hilary and Lorena Canary. His brothers are actor John Canary, who once had a role on All My Children, and Writer H. Glenn Canary (1934–2008). The brothers are purportedly great-great-nephews of Martha Jane Canary, a.k.a. Calamity Jane. He starred as an end on both offense and defense at Massillon Washington High School, where he graduated in 1956. The school honored him as a Distinguished Citizen 35 years later in 1991. He earned a football scholarship to the University of Cincinnati, where he was a three-year letterman from 1957 to 1959 and the recipient of the John Pease Award as the program's best lineman in his junior and senior years. Canary trained as a singer at the university's College of Arts and Sciences and received his bachelor's degree in music in 1960. He was picked by the Denver Broncos in the inaugural 1960 American Football League (AFL) draft. Commenting on the selection in a 2004 interview for the Archive of American Television, he said, "I thought they were out of their minds. I was 172 pounds, I wasn’t very fast, and I couldn’t catch a pass. They called me stone fingers." Instead of signing with the Broncos, he opted to head to New York City to become an actor. He served two years in the United States Army where he entered an All-Army Entertainment Contest in 1963. After ending his Service, Canary moved to Los Angeles to continue his acting career.