Ok I know of a study who agreed to read COC last year. She's still a study and is probably an unbaptized publisher by now.
Don't make the mistake of thinking that her reading that book (or any other book for that matter) will work some kind of magic.
Additionally, someone who is just studying with JWs will probably not grasp all the implications of COC.
I liked Slimboyfat's suggestions. Most of all you need to analyze what about the JWs is really "doing it" for her. There is no cookie-cutter approach.
For yourself, I would definitely read "Combatting Cult Mind Control" to better understand the phenomena involved. Have a non-judgmental talk with her on what she likes about the Witnesses and if you can understand which areas provide the most doubt for her that is key.
If you have no time to spend on her and she won't read anything, a good cassette for her to listen to is Randy Watters' "What Happened at Bethel in 1980?" available at http://freeminds.org
Read Jgnat's topic.
We "Unbelieving Mates" deal with this crap every day of our lives.