COL JOYE AND THE JOY BOYS
Vocal-Col Joye with the Graduates
and The New Notes
Don Fisk in a 1998 post to rec.music.rock-pop-r+b.1950s says that, according to Col Joye, American singer-songwriter Conway Twitty wrote this song for him. See also Ray Arthur’s 2004 post to rec.music.rock-pop-r+b.1950s in answer to my post.
Col Joye was a pioneering Aussie pop star of the rock’n’roll era (b. Colin Jacobsen, 1937) who in 1957 joined his brother Kevin’s jazz band that was to become Col Joye and the Joy Boys. He had ten Top 10 hits in the Sydney charts alone from May 1959 to May 1962, including four #1s, and was a star on television pop show Bandstand. Something of a legend in Australia, his rock’n’roll suit is on display at Sydney’s Powerhouse Museum.
Further reading: See, for example, the Col Joye biography at AllMusic.

Col Joye pinup from Chucklers’ Weekly, 22 Jan 1960.
Track on the 1969 Decca album Darling You Know I Wouldn’t Lie, accompanied by The Jordanaires.
The song was copyrighted in February 1960.

Sessionographies at Praguefrank’s site show two recordings of Bad Man by Conway Twitty:
1. In June 1961 at Kingston Studios in Scarborough, Ontario, unreleased until 1997 on The Rock ‘n’ Roll Years, a comprehensive Bear Family boxed set.
2. In February 1969 at Bradley’s Barn, Mount Juliet, TN, along with other songs for Darling, You Know I Wouldn’t Lie (1969), produced by Owen Bradley.