  Cross sections for the charm-production reactions $\bar p p \to \bar
\Lambda_c^- \Sigma_c^+$, $\bar \Sigma_c\Sigma_c$, $\bar \Xi_c\Xi_c$, and $\bar
\Xi_c'\Xi_c'$ are presented, for energies near their respective thresholds. The
results are based on a calculation performed in the meson-exchange framework in
close analogy to earlier studies of the J\"ulich group on the
strangeness-production reactions $\bar p p \to \bar \Lambda\Sigma$, $\bar
\Sigma\Sigma$, $\bar \Xi\Xi$ by connecting the two sectors via SU(4) flavor
symmetry. The cross sections are found to be in the order of $0.1 - 1$ $\mu b$
at energies of $100$ MeV above the respective thresholds, for all considered
channels. Complementary to meson-exchange, where the charmed baryons are
produced by the exchange of $D$ and $D^*$ mesons, a charm-production potential
derived in a quark model is employed for assessing uncertainties. The cross
sections predicted within that picture turned out to be significantly smaller.
