Recent evidence suggests that numerous similarities exist between the genomic landscapes of both conjunctival and cutaneous melanoma. Since alterations of several components of the MAP kinases, PI3K/mTOR, and cell cycle pathways have been reported in conjunctival melanoma, we decided to assess the sensitivity of conjunctival melanoma to targeted inhibition mostly of kinase inhibitors. A high content drug screening assay based on automated fluorescence microscopy was performed in three conjunctival melanoma cell lines with different genomic backgrounds with 489 kinase inhibitors and 53 other inhibitors. IC50 and apoptosis induction were respectively assessed for 53 and 48 compounds. The genomic background influenced the response to MAK and PI3K/mTOR inhibition, more specifically cell lines with BRAF ^V600E mutations were more sensitive to BRAF/MEK inhibition, while CRMM2 bearing the NRAS ^Q61L mutation was more sensitive to PI3k/mTOR inhibition. All cell lines demonstrated sensitivity to cell cycle inhibition, being more pronounced in CRMM2, especially with polo-like inhibitors. Our data also revealed new vulnerabilities to Hsp90 and Src inhibition. This study demonstrates that the genomic background partially influences the response to targeted therapy and uncovers a large panel of potential vulnerabilities in conjunctival melanoma that may expand available options for the management of this tumor.