The current emergency of the novel coronavirus SARS-CoV-2 urged the need for broad-spectrum antiviral drugs as the first line of treatment. Coronaviruses are a large family of viruses that already challenged humanity in at least two other previous outbreaks and are likely to be a constant threat for the future. In this work we developed a pipeline based on in silico docking of known drugs on SARS-CoV RNA-dependent RNA polymerase combined with in vitro antiviral assays on both SARS-CoV-2 and the common cold human coronavirus HCoV-OC43. Results showed that certain drugs displayed activity for both viruses at a similar inhibitory concentration, while others were specific. In particular, the antipsychotic drug lurasidone and the antiviral drug elbasvir showed promising activity in the low micromolar range against both viruses with good selective index.