A simple model is developed to treat the energy levels and spectroscopy of diatomic molecules inside C-60. The C-60 cage is treated as spherically symmetric, and the coupling to the C-60 vibrations is ignored. The remaining six degrees of freedom correspond to the vibrations and rotations of the diatomic molecule and the rattling vibration of the molecule inside the cage. By using conservation of angular momentum, we can remove two of these motions and simplify the calculations. The resulting energy levels are simple and can be labeled by a set of quantum numbers. The IR and Raman spectra look like those of gas-phase diatomic molecules at low temperatures. At higher temperatures, hot bands due to the low-frequency rattling mode appear, and the spectrum becomes congested, looking like a solution spectrum.