The "resolution of the identity" integral approximation applied to second-order many-body perturbation theory, or RI-MP2, method offers improved computational performance compared to traditional (exact) second-order perturbation theory calculations, but introduces a new auxiliary or "fitting basis set" into the method. We develop fitting-basis sets for use with the correlation consistent cc-pVDZ and cc-pVTZ atomic orbital basis sets for the atoms H-Ne. These fitting sets are designed to reproduce exact second-order results for a set of 32 test cases, including a variety of reaction energies, weak interactions, and electrostatic properties, to better than 1% error averaged across all tests and less than 2% error in any individual case. Although the RI-MP2 method is primarily targeted to large-scale calculations, it offers substantial performance improvements even for the small molecules used in these test cases.