I currently manufacture a product which I sell nationally (home
Furnishings) and would like to donate products for use in TV shows and
Movies. I am looking for contact info or "prop" departments of TV
networks or movie studios to submit proposals for free product in
exchange for use in their productions. I would like as specific
information as possible and not simply the mailing addresses of ABC,
NBC, CBS and HBO but departments or companies that collect props for
Use in set design.

Each production will have its own set designer. Their address would be
in care of the production office for the particular program. Every
week, on Tuesday, the Hollywood Reporter publishes a list of movies
and television that's currently in production.

You may also want to look into product placement. There are product
placement agencies that work for companies and make deals with
programs to get the goods into the show. Here's an overview of that
process: http://money.howstuffworks.com/product-placement.htm
Here is a list of product placement firms: 
http://www.la411.com/page-Listings-Category-1010-1180.html

Hollywood Cinema Production Resources runs a non-profit prop house:
http://www.hollywoodcpr.org/prophouse/

LA411, which is a compilation of resources for filmmakers, offers this
list of studio prop rentals. The addresses appear to be the generic
studio addresses, however.
http://www.la411.com/page-Listings-Category-1010-1181.html
There is also a list of prop-rental houses:
http://www.la411.com/page-Listings-Category-1010-1171.html
Also, set designers:
http://www.la411.com/page-Listings-Category-1011-1191.html

I hope this is helpful.
Search terms used: "prop rentals" "prop house" product placement