  Very light right-handed (RH) sneutrinos in the Next-to-Minimal Supersymmetric
Standard Model can be viable candidates for cold dark matter. We investigate
the prospects for their direct detection, addressing their compatibility with
the recent signal observed by the CoGeNT detector, and study the implications
for Higgs phenomenology. We find that in order to reproduce the correct relic
abundance very light RH sneutrinos can annihilate into either a
fermion-antifermion pair, very light pseudoscalar Higgses or RH neutrinos. If
the main annihilation channel is into fermions, we point out that RH sneutrinos
could naturally account for the CoGeNT signal. Furthermore, the lightest Higgs
has a very large invisible decay width, and in some cases the second-lightest
Higgs too. On the other hand, if the RH sneutrino annihilates mostly into
pseudoscalars or RH neutrinos the predictions for direct detection are below
the current experimental sensitivities and satisfy the constraints set by CDMS
and XENON. We also calculate the gamma ray flux from RH sneutrino annihilation
in the Galactic centre, including as an interesting new possibility RH
neutrinos in the final state. These are produced through a resonance with the
Higgs and the resulting flux can exhibit a significant Breit-Wigner
enhancement.
