In this paper, we apply the Stein's method in the context of point processes, namely when the target measure is the distribution of a finite Pois-son point process. We show that the so-called Kantorovich-Rubinstein distance between such a measure and another finite point process is bounded by the $L^1$-distance between their respective Papangelou intensities. Then, we deduce some convergence rates for sequences of point processes approaching a Poisson or a Cox point process.