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, $sigvlesssim 10^{-26},{rm cm^3/s}$, 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.
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