Stable, high-efficiency, and highly active electrocatalysts are critical for the conversion of renewable energy through overall water splitting. Our first-principles calculations identify two-dimensional conjugated metal-organic frameworks (2D c-MOFs) with dual metal sites as promising candidates for this process. Among them, PcCo-O8-Rh stands out as the best catalyst, with Rh serving as the active site for both the hydrogen evolution reaction (HER) and the oxygen evolution reaction (OER), resulting in a low ηHER/ηOER of -0.19/0.25 V. Our findings suggest that the HER/OER activity of PcTM-O8-TM' can be optimized through tensile strain, as it is related to the absorption strength of intermediates and the d-band center (εd) of the TM atom. This study presents a new family of 2D c-MOFs as high-performance bifunctional electrocatalysts for overall water splitting, paving the way towards sustainable energy conversion.