We report the measurements of $\gamma\gamma\rightarrow\eta_{c}(1S), \eta_{c}(2S)\rightarrow\eta'\pi^{+}\pi^{-}$ with $\eta'$ decays to $\gamma\rho$ and $\eta\pi^{+}\pi^{-}$ using 941 fb$^{-1}$ of data collected with the Belle detector at the KEKB asymmetric-energy $e^{+}e^{-}$ collider. First observation of $\eta_{c}(2S)\rightarrow\eta'\pi^{+}\pi^{-}$ with a significance 5.5$\sigma$ including systematic error is obtained. The products of the two-photon decay width and branching fraction of decays to $\eta'\pi^{+}\pi^{-}$ are determined for the $\eta_{c}(1S)$ and $\eta_{c}(2S)$, respectively. A new decay mode for the $\eta_c(1S)\rightarrow\eta'f_0(2080)$ with $f_0(2080)\rightarrow\pi^+\pi^-$ is observed with a statistical significance of 20$\sigma$. The cross section for $\gamma\gamma\rightarrow\eta'\pi^{+}\pi^{-}$ and $\eta'f_{2}(1270)$) are measured for the first time.