Charged hard-sphere mixtures consisting of two positively charged species and one negatively charged species (common anion mixtures) are used to represent binary mixtures of salts. Phase separation in the mixture is studied using the Gibbs free energy expression for common anion mixtures derived in paper I of this series. A detailed description of the dependence of the resulting phase diagrams on molecular size and charge of the species, and on the osmotic pressure of the mixture is presented. Binary mixtures of salts containing equal-sized ions exhibit type III phase behavior whereas binary mixtures of salts containing ions of unequal size exhibit either type II or type IV phase behavior. The type of phase behavior observed in binary mixtures of salts is characterized as a function of the critical pressures and critical volumes of the pure salts. Our results suggest that phase separation in mixtures of charged hard spheres is influenced by a competition between mixing effects (entropy), which encourage miscibility and ion-pairing effects (enthalpy), which encourage phase separation. Potential applications of the model to experimental systems are discussed.