Using a direct perturbation method, we investigate the stability of a diatomic molecule modelled by a weakly laser-driven Morse oscillator. It is shown that stationary state solution of the system is stable in the sense of Lyapunov and the periodical one possesses conditional stability, namely its stability depends on the initial conditions and system parameters. The corresponding sufficient and necessary conditions are established that indicate the stable states associated with some discrete energies. The results reveal how a diatomic molecule can be stabilized or dissociated with a weak laser, and demonstrate that the mathematical conditional stability works in the considered physical system.