  The CoGeNT experiment, dedicated to direct detection of dark matter, has
recently released excess events that could be interpreted as elastic collisions
of $\sim$10 GeV dark matter particles, which might simultaneously explain the
still mysterious DAMA/LIBRA modulation signals, while in conflict with results
from other experiments such as CDMS, XENON-100 and SIMPLE. It was shown that
5-15 GeV singlino-like dark matter candidates arising in singlet extensions of
minimal supersymmetric scenarios can fit these data; annihilation then mostly
proceeds into light singlet-dominated Higgs (pseudo)scalar fields. We develop
an effective Lagrangian approach to confront these models with the existing
data on cosmic-ray antiprotons, including the latest PAMELA data. Focusing on a
parameter space consistent with the CoGeNT region, we show that the predicted
antiproton flux is generically in tension with the data whenever the produced
(pseudo)scalars can decay into quarks energetic enough to produce antiprotons,
provided the annihilation S-wave is significant at freeze out in the early
universe. In this regime, a bound on the singlino annihilation cross section is
obtained, $\sigv\lesssim 10^{-26}\,{\rm cm^3/s}$, assuming a dynamically
constrained halo density profile with a local value of $\rho_\odot = 0.4\,{\rm
GeV/cm^3}$. Finally, we provide indications on how PAMELA or AMS-02 could
further constrain or detect those configurations producing antiprotons which
are not yet excluded.
