In this paper we consider a sequential meson emission mechanism for charmonium decays of the type Psi -> N Nbar m, where Psi is a generic charmonium state, N is a nucleon and m is a light meson. This decay mechanism, which may not be dominant in general, assumes that an NNbar pair is created during charmonium annihilation, and the light meson m is emitted from the outgoing nucleon or antinucleon line. A straightforward generalization of this model can incorporate intermediate N* resonances. We derive Dalitz plot event densities for the cases Psi = eta_c, J/psi, chi_c0, chi_c1} and psi and m = pi0, f0 and omega (and implicitly, any 0^{-+}, 0^{++} or 1^{--} final light meson). It may be possible to separate the contribution of this decay mechanism to the full decay amplitude through characteristic event densities. For the decay subset Psi -> p pbar pi0 the two model parameters are known, so we are able to predict absolute numerical partial widths for Gamma(Psi -> p pbar pi0). In the specific case J/psi -> p pbar pi0 the predicted partial width and M_{p pi0} event distribution are intriguingly close to experiment. We also consider the possibility of scalar meson and glueball searches in Psi -> p pbar f0. If the meson emission contributions to Psi -> N Nbar m decays can be isolated and quantified, they can be used to estimate meson-nucleon strong couplings {g_NNm}, which are typically poorly known, and are a crucial input in meson exchange models of the NN interaction. The determination of g_NNpi from Jpsi -> p pbar pi0 and the (poorly known) g_NNomega and the anomalous strong magnetic coupling kappa_{NNomega} from J/psi -> p pbar omega are considered as examples.
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