This is the name of one of the tracks on Pianologues
. A pianologue is "a performance at the piano, sometimes with a verbal accompaniment by the performer." This one is meant to be bucolic.
Many of the song titles that fill out Song Reader are references to older songs/sheet music. "Counting Daisy Petals" appears to have been a song from 1916 by Lytton Cox, though some phrases like this are common enough that Beck's use may not have been an actual reference.