(1) Cisplatin (CDDP) is used in melanoma chemotherapy, but it has many side effects. Hence, the search for natural substances that can reduce the dose of CDDP, and CDDP-related toxicity, is highly desired. Coumarins have many biological properties, including anticancer and antiproliferative effects. (2) An in vitro 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl-2H-tetrazolium bromide (MTT) assay on two human melanoma cell lines (FM55P and FM55M2) examined the antitumor properties of CDDP and five naturally occurring coumarins (osthole, xanthotoxin, xanthotoxol, isopimpinellin, and imperatorin). The antiproliferative effects produced by combinations of CDDP with the coumarins were assessed using type I isobolographic analysis. (3) The most potent anticancer properties of coumarins were presented by osthole and xanthotoxol. These compounds were characterized by the lowest median inhibitory concentration (IC) values relative to the FM55P and FM55M2 melanoma cells. Isobolographic analysis showed that for both melanoma cell lines, the combination of CDDP and osthole exerted synergistic and additive interactions, while the combination of CDDP and xanthotoxol exerted additive interactions. Combinations of CDDP with xanthotoxin, isopimpinellin, and imperatorin showed antagonistic and additive interactions in two melanoma cell lines. (4) The combination of CDDP and osthole was characterized by the most desirable synergistic interaction. Isobolographic analysis allows the selection of potential candidates for cancer drugs among natural substances.