We prove that the billiard map in a Bunimovich stadium has polynomial decay of correlations of the order of n-1. Ergodic Bunimovich-type billiards (two arcs not bigger than half a circle) that do not have trajectories with infinitely many consecutive bounces on straight lines satisfy the same property. We also prove that a very particular class of these billiards have polynomial decay of correlations of the order of n-2.