Using a sample of $1.06times10^{8}~psi(3686)$ events collected with the BESIII detector at BEPCII, the decays $eta_{c}(2S)to pbar{p}$ and $h_{c}to pbar{p}$ are searched for, where $eta_c(2S)$ and $h_c$ are reconstructed in the decay chains $psi(3686)
togammaeta_{c}(2S)$, $eta_{c}(2S)to pbar{p}$ and $psi(3686)topi^{0}h_{c}$, $h_{c}to pbar{p}$, respectively. No significant signals are observed. The upper limits of the product branching fractions are determined to be $mathcal{B}(psi(3686)togammaeta_c(2S))timesmathcal{B}(eta_{c}(2S)to pbar{p})<1.4times10^{-6}$ and $mathcal{B}(psi(3686)topi^0h_c)timesmathcal{B}(h_{c}to pbar{p})<1.3times10^{-7}$ at the 90% C.L.. The branching fractions for $chi_{cJ}to pbar{p}$ $(J=0,~1,~2)$ are also measured to be $(24.5pm0.8pm1.3,~8.6pm0.5pm0.5,~8.4pm0.5pm0.5)times10^{-5}$, which are the worlds most precise measurements.
