Bottom-up coarse-grained (CG) models are now regularly pursued to enable large length and time scale molecular simulations of complex, often macromolecular systems. However, predicting fluid phase equilibria using such models remains fundamentally challenging. A major problem stems from the typically low transferability of CG models beyond the densities and/or compositions at which they are parametrized, which is necessary if they are to describe distinct structural and thermodynamic properties unique to each phase, CG model transferability is compounded by the representation of the inherently multibody coarse interactions using pair potentials that neglect higher order effects. Here, we propose to construct transferable single site CG models of liquid mixtures by supplementing traditional CG pair interactions with local density potentials, which constitute a computationally inexpensive mean-field approach to describe many-body effects, in that site energies are modulated by the local solution environment. To illustrate the approach, we use intra- and interspecies local density potentials to develop CG models of benzene-water solutions that show impressive transferability in structural metrics (pair correlation functions, density profiles) throughout composition space, in contrast to pair-only CG representations. While further refinement may be necessary to represent more complex thermodynamic properties, like the liquid-liquid interfacial tension, the generality and improvement offered by the local density approach are highly encouraging for enabling complex phase equilibrium modeling using CG models.