Napoleon XIV (AKA Jerry Samuels) released "They're Coming to Take Me Away" in 1966. He had no second song, so they simply played the song backwards on the B-side.
A lot of singles simply feature an instrumental version of the A-side, for the same reason. Others would just grab a catalog song and record it to fill the space. Spike Milligan once sat quietly (and bored) humming and drumming his fingers in a recording studio for two minutes after he explained that he only had one song and "there's nothing on this side"
But I'm curious if anyone can point to an earlier example of a single with effectively only one song, and the B-side filled with just an instrumental, or some other example of the same song again? Or was Jerry the first just not to bother?