  Recently, the CoGeNT collaboration presented a positive signal for an annual
modulation in their data set. In light of the long standing annual modulation
signal in DAMA/LIBRA, we analyze the compatibility of both of these signal
within the hypothesis of dark matter (DM) scattering on nuclei, taking into
account existing experimental constraints. We consider the cases of elastic and
inelastic scattering with either spin-dependent or spin-independent coupling to
nucleons. We allow for isospin violating interactions as well as for light
mediators. We find that there is some tension between the size of the
modulation signal and the time-integrated event excess in CoGeNT, making it
difficult to explain both simultaneously. Moreover, within the wide range of DM
interaction models considered, we do not find a simultaneous explanation of
CoGeNT and DAMA/LIBRA compatible with constraints from other experiments.
However, in certain cases part of the data can be made consistent. For example,
the modulation signal from CoGeNT becomes consistent with the total rate and
with limits from other DM searches at 90% CL (but not with the DAMA/LIBRA
signal) if DM scattering is inelastic spin-independent with just the right
couplings to protons and neutrons to reduce the scattering rate on xenon.
Conversely the DAMA/LIBRA signal (but not CoGeNT) can be explained by
spin-dependent inelastic DM scattering.
