We discuss central exclusive production (CEP) of the tensor \(\chi_c(2^{+})\) meson in proton-(anti)proton collisions at Tevatron, RHIC and LHC energies. The amplitude for the process is derived within the \(k_t\)-factorisation approach. Differential and total cross sections are calculated for several unintegrated gluon distributions (UGDFs). We compare exclusive production of all charmonium states \(\chi_c(0^+),\,\chi_c(1^+)\) and \(\chi_c(2^+)\). Equally good description of the recent Tevatron data is achieved both with Martin-Ryskin phenomenological UGDF and UGDF based on unified BFKL-DGLAP approach. Unlike for Higgs production, the main contribution to the diffractive amplitude of heavy quarkonia comes from nonperturbative region of gluon transverse momenta \(Q_{\perp}<1\,\GeV\). At \(y \approx\) 0, depending on UGDF we predict the contribution of \(\chi_c(1^+,2^+)\) to the \(J/\Psi + \gamma\) channel to be comparable or larger than that of the \(\chi_c(0^+)\) one. This is partially due to a significant contribution from lower polarization states \(\lambda=0\) for \(\chi_c(1^+)\) and \(\lambda=0,\,\pm 1\) for \(\chi_c(2^+)\) meson. Corresponding theoretical uncertainties are discussed.