The RNA viruses SARS-CoV, SARS-CoV-2 and MERS-CoV encode the non-structural Nsp16 (2′-O-methyltransferase) that catalyzes the transfer of a methyl group from S-adenosylmethionine (SAM) to the first ribonucleotide in mRNA. Recently, it has been found that breaking the bond between Nsp16 and SAM substrate results in the cessation of mRNA virus replication. To date, only a limited number of such inhibitors have been identified, which can be attributed to a lack of an effective “recipe”. The aim of our study was to propose and verify a rapid and effective screening protocol dedicated to such purposes. We proposed four new indices describing structure-binding strength (structure–binding affinity, structure–hydrogen bonding, structure–steric and structure–protein–ligand indices) were then applied and shown to be extremely helpful in determining the degree of increase or decrease in binding affinity in response to a relatively small change in the ligand structure. After initial pre-selection, based on similarity to SAM, we limited the study to 967 compounds, so-called molecular chameleons. They were then docked in the Nsp16 protein pocket, and 10 candidate ligands were selected using the novel structure-binding affinity index. Subsequently the selected 10 candidate ligands and 8 known inhibitors and were docked to Nsp16 pockets from SARS-CoV-2, MERS-CoV and SARS-CoV. Based on the four new indices, the best ligands were selected and a new one was designed by tuning them. Finally, ADMET profiling and molecular dynamics simulations were performed for the best ligands. The new structure-binding strength indices can be successfully applied not only to screen and tune ligands, but also to determine the effectiveness of the ligand in response to changes in the target viral entity, which is particularly useful for assessing drug effectiveness in the case of alterations in viral proteins. The developed approach, the so-called chameleon strategy, has the capacity to introduce a novel universal paradigm to the field of drugs design, including RNA antivirals.