The COVID-19 pandemic has highlighted the urgent need for the identification of new antiviral drug therapies for a variety of diseases. COVID-19 is caused by infection with the human coronavirus SARS-CoV-2, while other related human coronaviruses cause diseases ranging from severe respiratory infections to the common cold. We developed a computational approach to identify new antiviral drug targets and repurpose clinically-relevant drug compounds for the treatment of a range of human coronavirus diseases. Our approach is based on graph convolutional networks (GCN) and involves multiscale host-virus interactome analysis coupled to off-target drug predictions. Cell-based experimental assessment reveals several clinically-relevant drug repurposing candidates predicted by the in silico analyses to have antiviral activity against human coronavirus infection. In particular, we identify the MET inhibitor capmatinib as having potent and broad antiviral activity against several coronaviruses in a MET-independent manner, as well as novel roles for host cell proteins such as IRAK1/4 in supporting human coronavirus infection, which can inform further drug discovery studies.