A coated article includes a temperable antireflection (AR) coating that utilizes medium and low index (index of refraction “n”) layers having compressive residual stress in the AR coating. In certain example embodiments, the coating may include the following layers from the glass substrate outwardly: silicon oxynitride (SiOxNy) medium index layer/high index layer/low index layer. In certain example embodiments, depending on the chemical and optical properties of the high index layer and the substrate, the medium and low index layers of the AR coating are selected to cause a net compressive residual stress and thus optimize the overall performance of the antireflection coating when the coated article is tempered and/or heat-treated.