  Consider a discrete uniformly elliptic divergence form equation on the $d$
dimensional lattice $\Z^d$ with random coefficients. In [3] rate of convergence
results in homogenization and estimates on the difference between the averaged
Green's function and the homogenized Green's function for random environments
which satisfy a Poincar\'{e} inequality were obtained. Here these results are
extended to certain environments with long range correlations. These
environments are simply related via a convolution to environments which do
satisfy a Poincar\'{e} inequality.
