Any gamecube mario party would be great, its basically a board game type thing if you ahvent played it, you "hit" a die and move so many spaces and at the end of the round you do a mini game. If you and her played it they would be the team things that you seem to be looking for. I have the first one and it is great, and i think theyre are around 3 for gamecube.
Super Smash Brothers Melee is my favorite gamecube game actually, im not sure wether i would recommend it to alot of people though, it takes a while to get used to and to be any good at it you have to have some skill. This is however not a co op game, there is a single player mode and a Vs. mode where you could fight each other, and plenty of unlockable characters to get though.
Get Mario Kart
. One of you can drive and the other can throw the various weapons you pick up, this is also one of my favorite gamecube games. You can unlock various cars in this game and me and my brother actually beat it together to get the last car, a real good multiplayer game. You can also race each other if you want to do that as well. Pretty hard in the later difficulties, if you are trying to unlock the cars though.