Shlemiel shlimazl

Laverne and Shirley used to open their comedy series with, "Shlemeil, Shemozzl ..." What does it mean?

I can help with the first two words of that bit:

From "The Joys of Yiddish" by Leo Rosten (Pocket Books, New York, 1996):

shlemiel, schlemiel, shlemiehl, shlemihl - carries a distinctive note of pity. In fact, a shlemiel is often the nebech's (sad sack, loser, nothing) twin brother. The classic definition goes: A shlemiel is always knocking things off a table; the nebech always picks them up.

shlimazl, shlimazel - chronically unlucky person; someone for whom nothing seems to go right or turn out well.

I imagine the rest is a children's song. Are they playing hopscotch when they sing it? I don't remember.