This very short one I used to sing to my daughter, Nancy, whom we called "the Binker" (after "Binky" i.e. pacifier). We also called her "Roo" (from "Nanneroo") and "Boo" (because it rhymed with "Roo", I think).

To (roughly) the tune of "H-A-double R-I-G-A-N spells Harrigan":

Nancy,
Nancy Binker Boo
You're the cutest Binker
Anybody ever knew!

Alex