We calculate the correction, due to nonlinear wave-wave interactions, to the Zel'dovich estimate for the turbulent diffusivity of magnetic fields in a model of two-dimensional magnetohydrodynamic turbulence in the presence of stable stratification. Such a model has some relevance to hydromagnetic turbulence in stellar interiors. The significance of this correction is that, unlike the lowest-order Zel'dovich balance, it is independent of the molecular resistivity eta and so will not vanish in the limit of a large magnetic Reynolds number, although the correction is O(sigma;{4}), where sigma is the wave slope, which necessarily is small. Thus, we are led to the counterintuitive result that the presence of stable stratification can actually increase the vertical flux of magnetic fields relative to that in 2D MHD turbulence without stratification.