This article deals with computation of all proportional-integral (PI) controllers which achieve the desired frequency-domain specifications namely, gain and phase margins (GPMs) of a traditional two-area load frequency control (LFC) system with constant communication delays. An efficient graphical method based on extracting the boundaries of stability regions in PI controller parameter space having user defined GPMs is proposed to obtain GPMs based stability regions. Regions are determined for a wide range of GPMs and time delay. The theoretical region boundaries are validated using a powerful numerical method known as the quasi-polynomial mapping-based root finder (QPmR) and time-domain simulations. Results indicate that the proposed scheme gives faster disturbance rejection and desired frequency response as compared to the recently developed scheme for LFC systems with communication delays.