We show that polygonal products of polycyclic-by-finite groups amalgamating central cyclic subgroups, with trivial intersections, are conjugacy separable. Thus polygonal products of finitely generated abelian groups amalgamating cyclic subgroups, with trivial intersections, are conjugacy separable. As a corollary of this, we obtain that the group A 1 *〈a1〉A 2 *〈a2〉 • • • *〈a m-1〉Am is conjugacy separable for the abelian groups Ai .