  Recently it has been shown that string instanton effects may give rise to
neutrino Majorana masses in certain classes of semi-realistic string
compactifications. In this paper we make a systematic search for supersymmetric
MSSM-like Type II Gepner orientifold constructions admitting boundary states
associated with instantons giving rise to neutrino Majorana masses and other L-
and/or B-violating operators. We analyze the zero mode structure of D-brane
instantons on general type II orientifold compactifications, and show that only
instantons with O(1) symmetry can have just the two zero modes required to
contribute to the 4d superpotential. We however discuss how the addition of
fluxes and/or possible non-perturbative extensions of the orientifold
compactifications would allow also instantons with $Sp(2)$ and U(1) symmetries
to generate such superpotentials. In the context of Gepner orientifolds with
MSSM-like spectra, we find no models with O(1) instantons with just the
required zero modes to generate a neutrino mass superpotential. On the other
hand we find a number of models in one particular orientifold of the Gepner
model $(2,4,22,22)$ with $Sp(2)$ instantons with a few extra uncharged
non-chiral zero modes which could be easily lifted by the mentioned effects. A
few more orientifold examples are also found under less stringent constraints
on the zero modes. This class of $Sp(2)$ instantons have the interesting
property that R-parity conservation is automatic and the flavour structure of
the neutrino Majorana mass matrices has a simple factorized form.
