In this contribution, we develop a coarse-graining methodology for mapping specific block copolymer systems to bead-spring particle-based models. We map the constituent Kuhn segments to Lennard-Jones particles, and establish a semi-empirical correlation between the experimentally determined Flory-Huggins parameter χ and the interaction of the model potential. For these purposes, we have performed an extensive set of isobaric-isothermal Monte Carlo simulations of binary mixtures of Lennard-Jones particles with the same size but with asymmetric energetic parameters. The phase behavior of these monomeric mixtures is then extended to chains with finite sizes through theoretical considerations. Such a top-down coarse-graining approach is important from a computational point of view, since many characteristic features of block copolymer systems are on time and length scales which are still inaccessible through fully atomistic simulations. We demonstrate the applicability of our method for generating parameters by reproducing the morphology diagram of a specific diblock copolymer, namely, poly(styrene-b-methyl methacrylate), which has been extensively studied in experiments.