I would like to write a letter to Joyce Randolph but I can't seem to find her address anywhere. If anyone has it, please send me a private message. Thanks.

You might want to try contacting Paul Brownstein. Maybe he can direct you to her agent/publicist:

http://www.tvclassics.com/

And if this is of help, Ms. Randolph, I.I.N.M., has been in the Manhattan telephone directory for years; I believe she's one of several "J. Randolph's" listed therein today.