  We investigate the possibility that right-handed (RH) sneutrinos and
gravitinos can coexist and explain the dark matter (DM) problem. We compare
extensions of the minimal supersymmetric standard model (MSSM) and the
next-to-MSSM (NMSSM) adding RH neutrinos superfields, with special emphasis on
the latter. If the gravitino is the lightest supersymmetric particle (LSP) and
the RH sneutrino the next-to-LSP (NLSP), the heavier particle decays to the
former plus left-handed (LH) neutrinos through the mixing between the scalar
partners of the LH and RH neutrinos. However, the interaction is suppressed by
the Planck mass, and if the LH-RH sneutrino mixing parameter is small, $\ll
O(10^{-2})$, a long-lived RH sneutrino NLSP is possible even surpassing the age
of the Universe. As a byproduct, the NLSP to LSP decay produces monochromatic
neutrinos in the ballpark of current and planned neutrino telescopes like
Super-Kamiokande, IceCube and Antares that we use to set constraints and show
prospects of detection. In the NMSSM+RHN, assuming a gluino mass parameter $M_3
= 3$ TeV we found the following lower limits for the gravitino mass $m_{3/2}
\gtrsim 1-600$ GeV and the reheating temperature $T_R \gtrsim 10^5 - 3 \times
10^7$ GeV, for $m_{\tilde{\nu}_R} \sim 10-800$ GeV. If we take $M_3=10$ TeV,
then the limits on $T_R$ are relaxed by one order of magnitude.
