Carol Channing guested on The Nanny in episode #1.2 - "Smoke Gets in Your Lies."
This episode appeared in the first season and aired on November 10, 1993.
A very short cameo where Ms. Channing appears onstage to sing her trademark song, "Hello Dolly" and is gruffly interrupted by Maxwell who was angry over Brighton's smoking in school and being kept in the dark about it.
Ms. Channing's one and only line was directed to Fran, "Watch out for this one - he's tough."