We present a calculation of the diffusion coefficient from a Hamiltonian for coupled coherent and incoherent transport with site-diagonal and off-diagonal stochastic fluctuations, which is not restricted to the usual white noise expression for the correlation between the fluctuating variables. Our result is applicable to any specific correlation and allows for long correlation times. We give examples for both monotonically decreasing and oscillating correlations. In the case of an exponential decay of the correlations the diffusion coefficient can be expressed by complete elliptic integrals.