A two axis accelerometer alone should be sufficient if the platform is not being excessively moved around and has a "top" side (will not be flipped over). The accelerometer should be positioned as closely to the center of the tilt as possible so the action of moving the platform doesn't cause excessive noise. It will work like an electric plumb bob and just like a real plumb bob you can't be swinging it around wildly.
If the platform is being moved about wildly then you should use a accelerometer and gyroscope combo, and read up on Kalman filtering or look into projects like MultiWii. It's not a simple problem combining accelerometer and gyro readings to keep track of orientation.