Within the last 15 years, two related coronaviruses (Severe Acute Respiratory Syndrome [SARS]-CoV and Middle East Respiratory Syndrome [MERS]-CoV) expanded their host range to include humans, with increased virulence in their new host. Coronaviruses were recently found to have little intrinsic disorder compared with many other virus families. Because intrinsically disordered regions have been proposed to be important for rewiring interactions between virus and host, we investigated the conservation of intrinsic disorder and secondary structure in coronaviruses in an evolutionary context. We found that regions of intrinsic disorder are rarely conserved among different coronavirus protein families, with the primary exception of the nucleocapsid. Also, secondary structure predictions are only conserved across 50–80% of sites for most protein families, with the implication that 20–50% of sites do not have conserved secondary structure prediction. Furthermore, nonconserved structure sites are significantly less constrained in sequence divergence than either sites conserved in the secondary structure or sites conserved in loop. Avoiding regions symptomatic of conformational flexibility such as disordered sites and sites with nonconserved secondary structure to identify potential broad-specificity antiviral targets, only one sequence motif (five residues or longer) remains from the >10,000 starting sites across all coronaviruses in this study. The identified sequence motif is found within the nonstructural protein (NSP) 12 and constitutes an antiviral target potentially effective against the present day and future coronaviruses. On shorter evolutionary timescales, the SARS and MERS clades have more sequence motifs fulfilling the criteria applied. Interestingly, many motifs map to NSP12 making this a prime target for coronavirus antivirals.