I would not use GENMOD for data which has a spatial covariance structure. GENMOD does not have any spatial covariance structures to choose from.
However, you could use the GLIMMIX procedure to model the residual covariance structure. GLIMMIX fits models from the exponential family so it is appropriate for fitting a logistic regression for a binary response. Also, the GLIMMIX procedure does allow a full set of spatial covariance structures.