We have used a recently introduced new tolerance factor τ to create a stability map of all possible A-site double perovskite titanates AA'Ti2O6 and niobates AA'Nb2O6. The predictive power of τ is relatively good based on comparisons with available experimental data for A-site double perovskites. We carried out quantum chemical calculations on two hypothetical double perovskite compositions CsScTi2O6 and YRbTi2O6, where τ predicts high probability for their existence. In both cases, we found limits in the predictive power of the new tolerance factor for ion combinations on the A and A' site which are very different in size. A difference in oxidation state may decrease the accuracy, as well. Overall, the A-site double perovskite stability mapping provides a starting point for the discovery of novel A-site double perovskites.