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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 decayscan be detected by the high-luminosity heavy-flavor experiments. At present,some of the semileptonic and nonleptonic $J/\Psi$ weak decays have beenmeasured 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 newphysics (NP). So we investigate the semileptonic and nonleptonic weak decays of$\psi(1S,2S)$ and $\eta_{c}(1S,2S)$ to $D_{(s)}$ within the covariantlight-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 theCLFQM, we predict and discuss some physical observables, such as the branchingratios, the longitudinal polarizations $f_{L}$ and the forward-backwardasymmetries $A_{FB}$. One can find that the Cabibbo-favored semi-leptonic decaychannels $\psi(1S,2S)\to D_{s}^{-}\ell^{+}\nu_{\ell}$ with $\ell=e,\mu$ and thenonleptonic decay modes $\psi(1S,2S)\to D_{s}^{-}\rho^{+}$ have relativelylarge branching ratios of the order $\mathcal{O}(10^{-9})$, which are mostlikely to be accessible at the future high-luminosity experiments.

Semileptonic and nonleptonic weak decays of $\psi(1S,2S)$ and $\eta_{c}(1S,2S)$ to $D_{(s)}$ in the covariant light-front approach