In a sequential study of rigidification of donating unit on its charge transfer towards accepting a coumarin unit, four donor-acceptor triphenylamine and N-phenyl carbazole based coumarin dyes were synthesized and characterized. The dyes exhibit positive solvatochromism which is well supported by linear as well as multilinear regression analysis. The intramolecular charge transfer characteristics were established using Generalized Mulliken-Hush (GMH), and frontier molecular orbital (FMO), Molecular electrostatic potential (MEP) plot analysis from optimized geometry. The detailed investigation of positive acidochromism is performed. The non-linear optical (NLO) properties of synthesized dyes were studied using solvatochromic and computational method. The linear polarizability, hyperpolarizability and second-order hyperpolarizability of the synthesized dyes were studied by time-dependent density functional theory computational method using three different functionals with the basis set 6–31 G (d).