Family Game Night, maybe?And it should be enjoyable for me
Whatever you usually play. Let her learn Call of Duty, etc.. by playing the story mode. Or if you like sports games play against her if you can do it without yelling eventually she should get good..
But if you want to make it totally about her just play something with kinect, if you have it hooked up, or a racing game/kiddie type game. The Wii is more fun for non-gamer type girls though. Make her get one of those and bring it to your house
unless you live with her