  In addition to the strong and electromagnetic decay modes, the $\psi(1S,2S)$
and $\eta_{c}(1S,2S)$ can also decay via the weak interaction. Such weak decays
can be detected by the high-luminosity heavy-flavor experiments. At present,
some of the semileptonic and nonleptonic $J/\Psi$ weak decays have been
measured at BESIII. Researching for these charmonium weak decays to $D_{(s)}$
meson can provide a platform to check of the standard model (SM) and probe new
physics (NP). So we investigate the semileptonic and nonleptonic weak decays of
$\psi(1S,2S)$ and $\eta_{c}(1S,2S)$ to $D_{(s)}$ within the covariant
light-front quark model (CLFQM). With form factors of the transitions
$\psi(1S,2S)\to D_{(s)}$ and $\eta_{c}(1S,2S)\to D_{(s)}$ calculated under the
CLFQM, we predict and discuss some physical observables, such as the branching
ratios, the longitudinal polarizations $f_{L}$ and the forward-backward
asymmetries $A_{FB}$. One can find that the Cabibbo-favored semi-leptonic decay
channels $\psi(1S,2S)\to D_{s}^{-}\ell^{+}\nu_{\ell}$ with $\ell=e,\mu$ and the
nonleptonic decay modes $\psi(1S,2S)\to D_{s}^{-}\rho^{+}$ have relatively
large branching ratios of the order $\mathcal{O}(10^{-9})$, which are most
likely to be accessible at the future high-luminosity experiments.
