"The term jukebox did not appear until the late 1930s and its origins are in dispute. Some believe it is derived from the African word jook, meaning to dance. Others link it to the juke joints—roadside bars located in the South and frequented by African Americans—that were popular at that time."
Alternativer Ansatz:
"Probably [an] alteration of English dialect jouk to cheat, deceive."
Eine Vermutung:
"Man könnte ableiten, dass ja keine echten Musiker in der Box sitzen."
Etymologische Herleitung:
"From dialect jukehouse brothel, from juke to have sexual intercourse with, of Atlantic Creole origin; akin to Jamaican English juk to poke, stab, Krio chuk."
(Quelle: http://dict.leo.org/forum/viewUnsolvedquery.php?idThread=560565&idForum=2&lang=de)