  The $J/{\psi}$ weak decays are rare but possible within the standard model of
elementary particles. Inspired by the potential prospects and sensitivity at
the future intensity frontier, the $J/{\psi}$ ${\to}$ $PP$ weak decays are
studied with the perturbative QCD approach, where $P$ denote the ground $SU(3)$
pseudoscalar meson. It is found that the $C$ parity violating $J/{\psi}$
${\to}$ ${\eta}^{({\prime})}{\eta}^{({\prime})}$ decays have relatively large
branching ratios, about the order of $10^{-11}$, which might be within the
measurement capability and sensitivity of the future STCF experiment.
