Discriminating two spatially separated sources is one of the most fundamental problems in imaging. Recent research based on quantum parameter estimation theory shows that the resolution limit of two incoherent point sources given by Rayleigh can be broken. However, in realistic optical systems, there often exists coherence in the imaging light field, and there have been efforts to analyze the optical resolution in the presence of partial coherence. Nevertheless, how the degree of coherence between two point sources affects the resolution has not been fully understood. Here, we analyze the quantum-limited resolution of two partially coherent point sources by explicitly relating the state after evolution through the optical systems to the coherence of the sources. In particular, we consider the situation in which coherence varies with the separation. We propose a feasible experiment scheme to realize the nearly optimal measurement, which adaptively chooses the binary spatial-mode demultiplexing measurement and direct imaging. Our results will have wide applications in imaging involving coherence of light.