A series of carboxamide derivatives of 6- and 7-substituted coumarins have been prepared by an original procedure starting from the corresponding 6- or 7-hydroxycoumarins which were alkylated with ethyl iodoacetate, and the obtained ester was converted to the corresponding carboxylic acids which were thereafter reacted with a series of aromatic/aliphatic/heterocyclic amines leading to the desired amides. The new derivatives were investigated as inhibitors of two enzymes, human carbonic anhydrases (hCAs) and soy bean lipoxygenase (LOX). Compounds 4a and 4b were potent LOX inhibitors, whereas many effective hCA IX inhibitors (KIs in the range of 30.2–30.5 nM) were detected in this study. Two compounds, 4b and 5b, showed the phenomenon of dual inhibition. Furthermore, these coumarins did not significantly inhibit the widespread cytosolic isoforms hCA I and II, whereas they were weak hCA IV inhibitors, making them hCA IX-selective inhibitors. As hCA IX and LOX are validated antitumor targets, these results are promising for the investigation of novel drug targets involved in tumorigenesis.