Due to their affordability and good catalytic activity for oxygen reactions, MOF-derived carbon composites containing metal alloys have piqued interest. However, during synthesis, MOFs have the disadvantage of causing significant carbon evaporation, resulting in a reduction of active sites and durability. This study proposes tailoring the molecular structure of MOFs by optimizing bipyridine and flexible 4-aminodiacetic terephthalic acid ligands, which have numerous coordination modes and framework structures, resulting in fascinating architectures. MOF frameworks having optimized N and O units are coordinated with Co and Ni ions to provide MOF precursors that are annealed at 700 °C in argon. The MOF-derived Co9S8/Co-Nx/CoNi/Ni3S2@CNS-4 catalyst exhibits excellent catalytic activity, revealing an ORR half-wave potential of 0.86 V and an overpotential (OER) of 196 mV at 10 mA cm-2, a potential gap of 0.72 V and a Tafel slope of 79 mV dec-1. The proposed strategy allows for the rational design of N-coordinated Co and CoNi alloys attached to ultrathin N, S co-doped graphitic carbon sheets to enhance bifunctional activity and sufficient active sites. Consequently, the zinc-air battery using the synthesized catalyst shows a high peak power density of 206.9 mW cm-2 (Pt/C + RuO2 116.1 mW cm-2), a small polarization voltage of 0.96 V after 370 h at 10 mA cm-2, and an outstanding durability of over 2400 cycles (400 h). The key contributions to the superior performance are the synergetic effects of the CoNi alloys plus the N,S-incorporated carbon skeleton, due to the small charge transfer resistances and enhanced active sites of CoNi, metal-S, and pyridinic N.