We present a numerical calculation for the static spin-symmetric and spin-antisymmetric local-field factors as a function of density in a two-dimensional (2D) unpolarized electron liquid. We use a recent analytical expression for the spin-resolved pair distribution function of a 2D electron liquid based on quantum Monte Carlo simulation data and accurate correlation energy as input to construct the local-field factors from the fluctuation-dissipation theorem. We obtain good agreement with data from quantum Monte Carlo studies of the 2D electron liquid over an extensive range of density.