"Rain, rain, go away, Come again some other day." Additional stanzas may have additional suggestions
My general assumption is that, if I learned something from other kids, with a tune, then it qualifies as "folk song." By that definition, this fits, silly as it is.
Aubrey's 1687 version, as quoted by the Baring-Goulds, is
Raine, raine, goe away,
Come again a Saterday. - RBW