Broad-spectrum antiviral drugs are urgently needed to stop the Coronavirus Disease 2019 pandemic and prevent future ones. The novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is related to the SARS-CoV and Middle East respiratory syndrome coronavirus (MERS-CoV), which have caused the previous outbreaks. The papain-like protease (PLpro) is an attractive drug target due to its essential roles in the viral life cycle. As a cysteine protease, PLpro is rich in cysteines and histidines, and their protonation/deprotonation modulates catalysis and conformational plasticity. Here, we report the pKa calculations and assessment of the proton-coupled conformational dynamics of SARS-CoV-2 in comparison to SARS-CoV and MERS-CoV PLpros using the recently developed graphical processing unit (GPU)-accelerated implicit-solvent continuous constant pH molecular dynamics method with a new asynchronous replica-exchange scheme, which allows computation on a single GPU card. The calculated pKa's support the catalytic roles of the Cys-His-Asp triad. We also found that several residues can switch protonation states at physiological pH among which is C270/271 located on the flexible blocking loop 2 (BL2) of SARS-CoV-2/CoV PLpro. Simulations revealed that the BL2 can open and close depending on the protonation state of C271/270, consistent with the most recent crystal structure evidence. Interestingly, despite the lack of an analogous cysteine, BL2 in MERS-CoV PLpro is also very flexible, challenging a current hypothesis. These findings are supported by the all-atom fixed-charge simulations and provide a starting point for more detailed studies to assist the structure-based design of broad-spectrum inhibitors against CoV PLpros.