A series of novel N-substituted 2-(2-oxo-2H-chromen-4-yloxy)propanamide derivatives were synthesized via converting the readily available 4-hydroxy coumarin to the corresponding ethyl 2-(2-oxo-2H-chromen-4-yloxy)propanoate followed by hydrolysis and then reacting with different substituted amines. The molecular structures of two representative compounds, that is, 3 and 5l were confirmed by single crystal X-ray diffraction study. All the compounds synthesized were evaluated for their cyclooxygenase (COX) inhibiting properties in vitro. The compound 5i showed balanced selectivity towards COX-2 over COX-1 inhibition and good docking scores when docked into the COX-2 protein.