Time dependent density functional theory (TD-DFT) calculations have been carried out to study the electronic structure and the optical properties of five coumarin based dyes: C343, NKX-2311, NKX-2586, NKX-2753 and NKX-2593. We have found out that the position and width of the first band in the electronic absorption spectra, the absorption threshold and the LUMO energy with respect to the conduction band edge are key parameters in order to establish some criteria that allow evaluating the efficiency of coumarin derivatives as sensitizers in Dye Sensitized Solar Cells (DSSC). Those criteria predict the efficiency ordering for the coumarin series in good agreement with the experimental evidence. Presumably, they might be used in the design of new efficient organic based DSSC.