In the first paper of this series [C. Avendano, T. Lafitte, A. Galindo, C. S. Adjiman, G. Jackson, and E. A. Muller, J. Phys. Chem. B 2011, 115, 11154] we introduced the SAFT-gamma force field for molecular simulation of fluids. In our approach, a molecular-based equation of state (EoS) is used to obtain coarse-grained (CG) intermolecular potentials that can then be employed in molecular simulation over a wide range of thermodynamic conditions of the fluid. The macroscopic experimental data for the vapor liquid equilibria (saturated liquid density and vapor pressure) of a given system are represented with the SAFT-VR Mie EoS and used to estimate effective intermolecular parameters that provide a good description of the thermodynamic properties by exploring a wide parameter space for models based on the Mie (generalized Lennard-Jones) potential. This methodology was first used to develop a simple single-segment CG Mie model of carbon dioxide (CO2) which allows for a reliable representation of the fluid-phase equilibria (for which the model was parametrized), as well as an accurate prediction of other properties such as the enthalpy of vaporization, interfacial tension, supercritical density, and second-derivative thermodynamic properties (thermal expansivity, isothermal compressibility, heat capacity, Joule Thomson coefficient, and speed of sound). In our current paper, the methodology is further applied and extended to develop effective SAFT-gamma CG Mie force fields for some important greenhouse gases including carbon tetrafluoride (CF4) and sulfur hexafluoride (SF6), modeled as simple spherical molecules, and for long linear alkanes including n-decane (n-C10H22) and n-eicosane (n-C20H42), modeled as homonuclear chains of spherical Mie segments. We also apply the SAFT-gamma methodology to obtain a CG homonuclear two-segment Mie intermolecular potential for the more challenging polar and asymmetric compound 2,3,3,3-tetrafluoro-1-propene (HFO-1234yf a novel replacement refrigerant with promising properties. The description of the fluid-phase behavior and the prediction of the other thermophysical properties obtained by molecular simulation using our SAFT-gamma CG Mie force fields are found to be of comparable quality (and sometimes superior) to that obtained using the more sophisticated all-atom (AA) and united-atom (UA) models commonly employed in the field. We should emphasize that though the focus of our current work is on simple homonudear models, the SAFT-gamma methodology is based on a group contribution methodology which is naturally suited to the development of more sophisticated heteronuclear models.