The predictive capability of coarse-grained (CG) models relies upon their ability to reproduce the relevant structural properties of accurate, though prohibitively expensive, atomistic models. The generalized Yvon–Born–Green (g-YBG) approach determines approximate potentials for accurate CG models directly from structural information. In this paper, we demonstrate the mechanism by which the g-YBG approach employs simple structural information to characterize and approximate the many-body potential of mean force. We then employ this approach to parameterize a three site CG model for liquid toluene. The resulting models are analyzed to determine their accuracy, sensitivity to changes in the CG mapping, and transferability to different temperatures.