  We study the Central Exclusive Production (CEP) of chi_cJ and eta_c mesons at
RHIC in proton-proton collisions. We consider the chi_cJ --> J/psi + gamma
decay channels and, recalling that the J_z=0 suppression of the J=1,2 states
can be compensated by their larger branchings to J/psi + gamma, present
predictions of rates and distributions for chi_c(0,1,2) production. Particular
attention is paid to the impact of p_t cuts applied to the outgoing protons,
which can influence the relative rates significantly. The distribution in the
azimuthal angle difference between the outgoing protons and the proton p_t^2 is
also studied, and shown to depend sensitively on the spin and parity of the
centrally produced meson, as well as being affected by the soft survival
factors, S^2. Two- and four-body decays, which are particularly relevant for
chi_c0 production, are also considered. We show that in the two-body case,
backgrounds from `direct' QCD production based on both perturbative and
non-perturbative models are expected to be under control.
