  In this paper we investigate the $(g-2)_\mu$ discrepancy in the context of
the R-parity conserving next-to-minimal supersymmetric Standard Model plus
right-handed neutrinos superfields. The model has the ability to reproduce
neutrino physics data and includes the interesting possibility to have the
right-handed sneutrino as the lightest supersymmetric particle and a viable
dark matter candidate. Since right-handed sneutrinos are singlets, no new
contributions for $\delta a_{\mu}$ with respect to the MSSM and NMSSM are
present. However, the possibility to have the right-handed sneutrino as the
lightest supersymmetric particle opens new ways to escape Large Hadron Collider
and direct detection constraints. In particular, we find that dark matter
masses within $10 \lesssim m_{\tilde{\nu}_{R}} \lesssim 600$ GeV are fully
compatible with current experimental constraints. Remarkably, not only spectra
with light sleptons are needed, but we obtain solutions with $m_{\tilde{\mu}}
\gtrsim 600$ GeV in the entire dark matter mass range that could be probed by
new $(g-2)_\mu$ data in the near future. In addition, dark matter direct
detection experiments will be able to explore a sizable portion of the allowed
parameter space with $m_{\tilde{\nu}_{R}} \lesssim 300$ GeV, while indirect
detection experiments will be able to probe a much smaller fraction within $200
\lesssim m_{\tilde{\nu}_{R}} \lesssim 350$ GeV.
