The nucleocapsid protein (NP) is one of the main proteins out of four structural proteins of coronaviruses including the severe acute respiratory syndrome coronavirus 2, SARS-CoV-2, discovered in 2019. NP packages the viral RNA during virus assembly and is, therefore, indispensable for virus reproduction. NP consists of two domains, i.e., the N- and C-terminal domains. RNA-binding is mainly performed by a binding pocket within the N-terminal domain (NTD). NP represents an important target for drug discovery to treat COVID-19. In this project, we used the Vina LC virtual drug screening software and a ZINC-based database with 210,541 natural and naturally derived compounds that specifically target the binding pocket of NTD of NP. Our aim was to identify coronaviral inhibitors that target NP not only of SARS-CoV-2 but also of other diverse human pathogenic coronaviruses. Virtual drug screening and molecular docking procedures resulted in 73 candidate compounds with a binding affinity below −9 kcal/mol with NP NTD of SARS-CoV-1, SARS-CoV-2, MERS-CoV, HCoV-OC43, HCoV-NL63, HoC-229E, and HCoV-HKU1. The top five compounds that met the applied drug-likeness criteria were then tested for their binding in vitro to the NTD of the full-length recombinant NP proteins using microscale thermophoresis. Compounds (1), (2), and (4), which belong to the same scaffold family of 4-oxo-substituted-6-[2-(4a-hydroxy-decahydroisoquinolin-2-yl)2H-chromen-2-ones and which are derivates of coumarin, were bound with good affinity to NP. Compounds (1) and (4) were bound to the full-length NP of SARS-CoV-2 (aa 1–419) with Kd values of 0.798 (±0.02) µM and 8.07 (±0.36) µM, respectively. Then, these coumarin derivatives were tested with the SARS-CoV-2 NP NTD (aa 48–174). Compounds (1) and (4) revealed Kd-values of 0.95 (±0.32) µM and 7.77 (±6.39) µM, respectively. Compounds (1) and (4) caused low toxicity in human A549 and MRC-5 cell lines. These compounds may represent possible drug candidates, which need further optimization to be used against COVID-19 and other coronaviral infections.