  Resonance based numerical schemes are those in which cancellations in the
oscillatory components of the equation are taken advantage of in order to
reduce the regularity required of the initial data to achieve a particular
order of error and convergence. We investigate the potential for the derivation
of resonance based schemes in the context of nonlinear stochastic PDEs. By
comparing the regularity conditions required for error analysis to traditional
exponential schemes we demonstrate that at orders less than $ \mathcal{O}(t^2)
$, the techniques are successful and provide a significant gain on the
regularity of the initial data, while at orders greater than $ \mathcal{O}(t^2)
$, that the resonance based techniques does not achieve any gain. This is due
to limitations in the explicit path-wise analysis of stochastic integrals. As
examples of applications of the method, we present schemes for the
Schr\"odinger equation and Manakov system accompanied by local error and
stability analysis as well as proof of global convergence in both the strong
and path-wise sense.
