While planar Fermi superfluids form Abrikosov vortex lattices under magnetic or effective gauge fields, spherical geometry forbids perfect lattices above 20 vortices. We characterize approximate vortex lattices of atomic Fermi superfluids under an effective monopole field on a spherical surface as an analogue of the planar vortex-lattice problem by two constructions based on the Ginzburg-Landau theory. The first one is geometric and uses approximate lattices, including the random, geodesic-dome, and Fibonacci lattices, as scaffolds to construct the vortices from the degenerate monopole harmonics. The second one generalizes J. Phys. A 39, 2499 (1996) and minimizes the free energy by numerically adjusting the coefficients to find the solution with the minimal Abrikosov parameter. We have verified that the vortices from both constructions are zeros of the order parameter with circulating currents around the vortex cores and the Poincare–Hopf theorem is satisfied. As the number of vortices increases, the Abrikosov parameters of both the Fibonacci-lattice and minimization solutions extrapolate to the planar value. We briefly discuss implications for ultracold atoms in thin spherical-shell geometry.