  We study exclusive production of scalar $\chi_{c0}\equiv \chi_c(0^{++})$ and
pseudoscalar $\eta_c$ charmonia states in proton-proton collisions at the LHC
energies. The amplitudes for $gg \to \chi_{c0}$ as well as for $gg \to \eta_c$
mechanisms are derived in the $k_{T}$-factorization approach. The $p p \to p p
\eta_c$ reaction is discussed for the first time. We have calculated rapidity,
transverse momentum distributions as well as such correlation observables as
the distribution in relative azimuthal angle and $(t_1,t_2)$ distributions. The
latter two observables are very different for $\chi_{c0}$ and $\eta_c$ cases.
In contrast to the inclusive production of these mesons considered very
recently in the literature, in the exclusive case the cross section for
$\eta_c$ is much lower than that for $\chi_{c0}$ which is due to a special
interplay of the corresponding vertices and off-diagonal UGDFs used to
calculate the cross sections. We present the numerical results for the key
observables in the framework of potential models for the light-front quarkonia
wave functions. We also discuss how different are the absorptive corrections
for both considered cases.
