In this paper, we presented a new machine-learning framework for predicting exciton coupling between molecules. Our framework uses a graph neural network (GNN) that predicts atomic transition charges (ATCs) for atoms in a molecule. Excitonic coupling between pairs of molecules is then calculated by application of the ATC approximation, which simply involves summing a series of Coulomb-like terms. Our framework generalizes well across a wide range of molecules, thereby overcoming the primary limitation of previous machine-learning models of exciton coupling: the restriction to specific molecule types. Moreover, our framework could successfully predict exciton couplings for several fusedring electron acceptor (FREA) molecules, which are of high importance in current organic solar cell research. The framework breaks down when attempting to predict very small couplings, and this was traced to the occurrence of error propagation in the ATC method. In regimes where excitonic coupling is stronger, our framework is robust.