Comparison of evolution among related viruses can provide insights into shared adaptive processes, for example following host switching to a mutual host species. Whilst phylogenetic methods can help identify mutations that may be important for evolutionary processes such as adaptation to a new host, these can be enhanced by positioning candidate mutations to known functional sites on protein structures. Over the past two decades, three zoonotic betacoronaviruses have significantly impacted human public health: SARS-CoV-1, MERS-CoV and SARS-CoV-2, whilst two other betacoronaviruses, HKU1 and OC43, have circulated endemically in the human population for over 100 years. In this study, we use a comparative approach to prospectively search for potentially evolutionarily-relevant mutations within the Orf1ab and S genes across betacoronavirus species that have demonstrated sustained human-to-human transmission (HKU1, OC43, SARS-CoV-1 and SARS-CoV-2). We used a combination of molecular evolution methods to identify 30 sites that display evidence of homoplasy and/or stepwise evolution, that may be suggestive of adaptation across emerging and endemic betacoronaviruses. Of these, seven sites also display evidence of being selectively relevant. Drawing upon known protein structure data, we find that four of the identified mutations [18121 (exonuclease/27), 21623 (spike/21), 21635 (spike/25) and 23948 (spike/796), in SARS-CoV-2 genome coordinates] are proximal to regions of known functionality. Our results provide a molecular-level context for common evolutionary pathways that betacoronaviruses may undergo during adaptation to the human host.