In this paper we show how to construct an algorithm to sample the stationary distribution of a random walk over ${1,...,N}^d$ with forbidden arcs. This algorithm combines the rejection method and coupling from the past of a set of trajectories of the Markov chain that generalizes the classical sandwich approach. We also provide a complexity analysis of this approach in several cases showing a coupling time in $O(N^2 d log d )$ when no arc is forbidden and an experimental study of its performance.