The Belafonte "Suzanne" is a completely different song:

Every night when the sun goes down,
...Hang my head in mournful cry.
Suzanne...Suzanne...Suzanne...you're gone.

It's on his second album, Belafonte, and also on his Belafonte Returns to Carnegie Hall.
www.cdnow.com shows a number of recordings of songs with the name "Suzanne." I'll bet most of them are the song written by Leonard Cohen, but the Belafonte recording is not.
-Joe Offer-