In recent years, polar magnets M₂Mo₃O₈(M:3d transition metal) have emerged as a research focus in condensed matter physics and materials science due to their unique crystal structures, multiple continuous magnetoelectric-coupled state transitions, and potential applications. Notably, Co₂Mo₃O₈ exhibits a significant second-order nonlinear magnetoelectric coupling effect in its ground state, corresponding to a unique microscopic magnetoelectric coupling mechanism and practical value. In this work, based on a molecular field phenomenological model, we construct two distinct antiferromagnetic sublattices for the Co₂Mo₃O₈ system and present the temperature-dependent variations of its spontaneous magnetic moment, spin-induced ferroelectric polarization, first-order linear magnetoelectric coupling coefficient, and second-order nonlinear magnetoelectric coupling coefficient. Particularly, the parameters t=-1 and o=-0.96 indicate distinct exchange energies between the magnetic sublattices associated with tetrahedra (Co_t) and octahedra (Co_o). The Co²⁺ ions in these two sublattices, which were characterized by different molecular field coefficients, synergistically mediate a spin-induced spontaneous polarization of P_S~0.12 μC/cm² through the exchange striction mechanism and p-d hybridization mechanism in Co₂Mo₃O₈. In addition, the significant second-order magnetoelectric coupling effect with a coefficient peaking at 70x10^-19 s/A near the T_N in Co₂Mo₃O₈, where this coefficient is significantly larger than those of isostructural Fe₂Mo₃O₈ (1.81x10^-28 s/A) and Mn₂Mo₃O₈, implies that this enhancement primarily arises from the weaker inter-sublattice antiferromagnetic exchange between its two sublattices, leading to a stabilizes metastable spin configuration. This also indicates that the Co₂Mo₃O₈ system possesses stronger irreversibility stability and exhibits a pronounced magnetoelectric diode effect, providing a solid theoretical and computational foundation for the development of magnetoelectric diodes.<