Measuring the change of angle on any plane
You can get very low drift by buying a very good gyro.. for example a ring-laser or fiber-optic gyro, but the cost may be prohibitive for your application (I'm currently working with a triad that costs as much as a decent automobile), and the very good ones tend to have export controls and other associated inconveniences since they have obvious dual-use capability in weapon inertial navigation applications. 

If you only want to measure small deviations from horizontal (deviation from the gravity vector), there are interesting clinometer (inclinometer) methods that use electrodes disposed in a dielectric fluid, sort of an electronic 2-D spirit level. Since they're an absolute measurement you can zero them out and they'll not continuously drift (other than the usual 1/f type thermal drift).