Two-photon absorption (2PA) spectroscopy is a robust bioimaging tool that depends on the determined cross-sections (σ^2PA). The absorption of both photons occurs simultaneously with equivalent (degenerate) or different (non-degenerate) photon energies, D-2PA and ND-2PA, respectively. The former has been investigated experimentally and computationally for many systems, while the latter remains relatively unexplored computationally and limited experimentally. In this study, response theory using time-dependent density functional theory (TD-DFT) and the 2-state model (2SM) have been utilized to investigate σ^D-2PA and σ^ND-2PA for the excitation to the lowest energy singlet state (S₁) of coumarin, coumarin 6, coumarin 120, coumarin 307, and coumarin 343. Solvents involved were methanol (MeOH), chloroform (ClForm), and dimethylsulfoxide (DMSO), where the latter leads to the largest σ^2PA. Values of σ^2PA are largest for coumarin 6 and lowest for coumarin, which illustrates the effect of substituents. The 2SM clarifies how the largest cross-sections correspond to molecules with the largest transition dipole moments, μ₀₁. In general, σ^D-2SM computations agree with σ^D-2PA. Moreover, σ^ND-2SM are in qualitative agreement with σ^ND-2PA with comparable enhancement relative to σ^D-2PA. Overall, σ^ND-2PA are larger than σ^D-2PA where the increase is in the range of 22% to 49%, depending on the coumarin as well as the relative energies of the two photons. This work aids in future investigations into various fluorophores to understand their photophysical properties for ND-2PA.