  We present predictions for the diffractive production of $\chi$ mesons in the
central rapidity region usually covered by collider detectors. The predicted
cross sections are based on the Bialas-Landshoff formalism for both exclusive
and inclusive production and makes use of the DPEMC Monte-Carlo simulation
adapted with kinematics appropriate for small-mass diffractive production. We
compare generator-level results with a CDF measurement for exclusive $\chi$
production, and study background and other scenarios including the contribution
of inclusive $\chi$ production. The results agree with the Tevatron data and
are extrapolated, highlighting the exclusive $\chic$ production at LHC
energies. A possible new measurement at the Tevatron using the D{\O}forward
detectors is investigated, taking advantage of the dominance of exclusive
production for high enough diffractive mass fraction.
