Inhibitors of monoamine oxidases (MAOs) are of interest for the treatment of neurodegenerative disorders and other human pathologies. In this frame, the present work describes different synthetic strategies to obtain MAO inhibitors via the coupling of the aminocoumarin core with arylsulfonyl chlorides followed by copper azide-alkyne cycloaddition, leading to coumarin–sulfonamide–nitroindazolyl–triazole hybrids. The nitration position on the coumarin moiety was confirmed through nuclear magnetic resonance spectroscopy and molecular electron density theory in order to elucidate the molecular mechanism and selectivity of the electrophilic aromatic substitution reaction. The coumarin derivatives were evaluated for their inhibitory potency against monoamine oxidases and cholinesterases. Molecular docking calculations provided a rational binding mode of the best compounds in the series with MAO A and B. The work identified hybrids 14a–c as novel MAO inhibitors, with a selective action against isoform B, of potential interest to combat neurological diseases.