Coarse-grained (CG) models provide a highly efficient computational means for investigating complex processes that evolve on large length-scales or long time-scales. The predictive capability of these models relies upon their ability to reproduce the relevant structural properties of accurate, though prohibitively expensive, atomistic models. The many-body potential of mean force (PMF) is the appropriate potential for a CG model that quantitatively reproduces the structure of an underlying atomistic model. Because this PMF cannot be readily calculated or simulated, several methods attempt to systematically approximate this PMF with relatively simple molecular mechanics potentials. Recently, we have proposed a generalized-Yvon–Born–Green (g-YBG) approach to determine approximate potentials for accurate CG models directly from structural information. In the present work, we demonstrate the mechanism by which the g-YBG approach employs simple structural information to characterize and approximate the many-body PMF. We then employ this approach to parameterize a three site CG model for liquid toluene. We demonstrate that this model accurately reproduces the structural properties of an all-atom model. Moreover, using this model system, we demonstrate the variational nature of the method and investigate the sensitivity of the model to the CG mapping. Finally, we briefly investigate the transferability of the CG model to different temperatures.