Steve Gardham wrote:

There was also a two-ball/skipping rhyme which starts
Alla-balla-boushka King of the Jews

In the Ballad Index as "Nebuchadnezzar's Wife"; I've seen versions with Nebuchadnezzar, Holy Moses, Thomas a Didymus, Pontius Pilate, and others.

But one should also check the big mess that I filed under "Ickie Bickie Soda Cracker," which floats in all sorts of direction and relates to "My Mother and Your Mother."

That's apart from the link to "Coulter's Candy," of course.