We study the effects of Coulomb screening on the second-order dc response in finite-size diffusive conductors. Starting from the Boltzmann equation supplemented by the self-consistent electrostatic field, we develop a kinetic theory of the inverse Faraday effect for a two-dimensional disk driven by a circularly polarized ac electric field. In this formulation, the first-order charge modulation and the induced electric field are coupled through the Coulomb interaction, and the self-consistent first-order solution determines the nonlinear source for the second-order dc circulating current responsible for the induced magnetic moment. The radial problem is solved numerically using an angular-harmonic expansion and the Chebyshev collocation method. It is shown that in the non-self-consistent approximation the frequency dependence of the second-order dc response has a maximum when the diffusion length associated with the radiation frequency becomes comparable to the sample radius. This behavior is found to be strongly modified by self-consistent screening. We demonstrate that Coulomb screening shifts the maximum of the dc response to a higher drive frequency and suppresses the peak amplitude. This behavior is observed consistently for the area-integrated circulating current and the induced magnetic moment. The obtained results clarify the limitations of the non-self-consistent description of the inverse Faraday effect and show that Coulomb self-consistency is crucial for quantitative predictions of optically induced dc magnetization in finite-size diffusive conductors.