Nonleptonic two-body $$B_c$$ B c decays including radially excited $$\psi (2S)$$ ψ ( 2 S ) or $$\eta _c(2S)$$ η c ( 2 S ) mesons in the final state are studied using the perturbative QCD approach based on $$k_T$$ k T factorization. The charmonium distribution amplitudes are extracted from the $$n = 2, l = 0$$ n = 2 , l = 0 Schrödinger states for the harmonic oscillator potential. Utilizing these distribution amplitudes, we calculate the numerical results of the $$B_c\rightarrow \psi (2S),\eta _c(2S)$$ B c → ψ ( 2 S ) , η c ( 2 S ) transition form factors and branching fractions of $$B_c\rightarrow \psi (2S)\pi , \eta _c(2S)\pi $$ B c → ψ ( 2 S ) π , η c ( 2 S ) π decays. The ratio between two decay modes $$B_c\rightarrow \psi (2S)\pi $$ B c → ψ ( 2 S ) π and $$B_c\rightarrow J/\psi \pi $$ B c → J / ψ π is compatible with the experimental data within uncertainties, which indicates that the harmonic-oscillator wave functions for $$\psi (2S)$$ ψ ( 2 S ) and $$\eta _c(2S)$$ η c ( 2 S ) work well. It is found that the branching fraction of $$B_c\rightarrow \eta _c(2S)\pi $$ B c → η c ( 2 S ) π , which is dominated by the twist-3 charmonium distribution amplitude, can reach the order of $$10^{-3}$$ 10 - 3 . We hope it can be measured soon in the LHCb experiment.