It's not SF, but it is a kids book and it's old enough (1951): Centerburg Tales by Robert McCloskey.
The chapter you're describing sounds like "Pie and Punch and You-Know-Whats" which has the following description on Wikipedia:
A new record on the jukebox in Uncle Ulysses's lunchroom has a song whose catchiness is such that nobody who hears it is able to stop singing.
Some bits of reviews and snippets on Google Books suggest the song is about donuts (and their holes) and that there is a simple trick used to undo the song.