Sub-grid models are key tools to accurately describe the physical processes at play in a system when high-resolution simulations are not feasible. We previously developed a sub-grid model for pitch-angle diffusion in hybrid-Vlasov simulations of Earth's magnetosphere. However, a more precise description of the pitch-angle diffusion coefficient is required to apply this model to global simulations. In this study, we use an existing method to parametrize pitch-angle diffusion coefficients from monotonic distribution functions and adapt it to bi-Maxwellian distributions. We determine these coefficients for various values of the ion temperature anisotropy and plasma β∥. We use these newly parametrized coefficients in our sub-grid model and show that it accurately models reduction of temperature anisotropy in both local simulations and global simulations of the Earth's magnetosphere, while using minimal computational resources.