We present a first-principles study of the 2D carbonyl stretch infrared spectra of dimanganese decacarbonyl, Mn-2(CO)(10), and its photoproducts, Mn-2(CO)(9) and Mn(CO)(5). The corresponding multidimensional anharmonic potential energy surfaces are computed via density functional theory up to fourth-order in the normal mode coordinates. The anharmonic shifts are computed using vibrational perturbation theory and benchmarked against results obtained by diagonalizing the vibrational Hamiltonian in the case of Mn(CO)(5). The importance of accounting for couplings between the photoactive and photoinactive CO stretches as well as for contributions that arise from fourth-order force constants is demonstrated. The 2D spectra are compared with experiment in the case of Mn-2(CO)(10). The reasonable agreement between theory and experiment suggests that an approach combining density functional theory with vibrational perturbation theory can provide a useful route for computing 2D infrared spectra, particularly in cases where direct diagonalization of the vibrational Hamiltonian is not feasible.