While we are trying to dethrone Rain here, Sandstorm is still a threat to sun (including stealth rock). Because of this, one of our types could be Grass or Fighting, to counter Tyranitar and Stealth Rock. Right now, Grass seems like an excellent idea, as it resits Rain abusers (not counting ice coverage), Sandstorm abusers, and Stealth Rock, while being synergetic with Sun.
I'm not absolutely sure about the second type, but ice is underused, deals with dragons, and cancels the Ice weakness.
So right now I'm considering a Grass/Ice.
EDIT: This would give CAP5 a x4 weakness to Fire, but that would also help in dethroning the "Big Four", by encouraging Fire types.