Via the Kansas City Star:
...But “Dilly Dilly” wasn’t a pure stroke of genius out of thin air. According to dictionary.com, the origins of “dilly” are in a shortening of the word “delightful” or “delicious,” probably from the 1930s. On its own, it has come to mean “something or someone regarded as remarkable or unusual.”File this one away next to the "It's Wednesday, Gary." "I know that Janet" one as gold.