We give predictions for diffractive heavy flavour production at the Tevatron and the LHC in leading--order approximation. In the framework of these studies we use three different models for the partonic structure of the Pomeron recently proposed by Stirling and Kunszt. These Pomeron models are, despite being fitted to the same diffractive deep inelastic HERA data, very different in their parton content and taken together provide a powerful tool to probe the structure of the Pomeron. All models satisfy GLAP evolution and show a significant $Q^2$ dependence. We give numerical predictions for single as well as double diffractive cross sections assuming a Donnachie--Landshoff--type Pomeron flux factor.