In this paper we use the generic van der Waals equation of state to define the free volume of liquids along the liquid-vapor coexistence line (liquids curve) in the case of liquid argon and along three isotherms in the high-pressure regime in the case of liquid methane. With the free volume computed from the cavity function obtained by means of a Monte Carlo simulation method, we have calculated the self-diffusion coefficients of liquid argon and liquid methane. The Cohen-Turnbull free volume theory is used to calculate them. With the empirical parameter appearing in the Cohen-Turnbull theory suitably adjusted, the theoretical and experimental values of the self-diffusion coefficients agree very well with regard to the density and temperature dependence for the cases of available data compared. A pair of analytic formulas for density dependence of the self-diffusion coefficient is obtained by using the approximate cavity functions for hard spheres and tested against the experimental data on methane. A comparison of the analytic formulas with experiment is also very good.