Technically, she isn't a n00b, she's a newb - as in Newbie, or new person trying to learn. Only if she plays for an extended period, doesn't learn how to actually play, and blames everyone else for her crapicity and then calls everyone else n00bs and/or f@gs when she's actually the one bringing the game down, has she entered n00b-town.
I'm going to be honest, I wouldn't do too much co-op if you know you don't have the patience to sit there and defuse the situation if she becomes overly frustrated. If you know you wont be able to play co-op without considering punching her and then punching yourself, there is nothing wrong with having her play singer-player games that you've played yourself, consider too easy, and being there to help her when she has a question - IF that is the best option for you. Key is: Patience, understanding, and no raging.lol.
But it's always great to find out what she likes, as everyone else has already stated, and go from there.Such as; if she likes a lot of medieval fantasy or L.O.T.R, then go for wrpgs (with tutorials and/or whole tutorial levels). If she likes anime, find her a few jrpgs (with tutorials and/or whole tutorial levels). If those are seeming too advanced, you may have to start with simple/fun sidescrollers - you could try the Little Big Planet series. I love that series.
Really, anything with a tutorial, and an 'easy' setting in difficulty to start with. Also, tell her she should also play at home - or by herself and see if she can overcome the difficulties of some games by herself. Since that will force her to try and figure out new ways to beat it, instead of continuously asking you a multitude of questions. Practice makes perfect, blah , blah, blargh.