"The earliest source (so far) is Learning to Write by Reed Smith, Bill Paxton, William Paxton, and Basil G. Meserve, 3rd ed. Heath, 1951. Google only gives a snippet view, but that's enough: '[the] chief co-ordinating conjunctions are sometimes called the fanboy words.' (p. 398)."And then the full acronym:
"The next work found in Google Books, and the first that actually gives FANBOYS as an acronym, is dated 1970:
Gertrude B. Corcoran, Language arts in the elementary school: a modern linguistic approach, Ronald Press Co. 1970, p. 140:
'Coordinating conjunctions can be remembered by thinking of the acronym FANBOYS'."