Game engines typically do approximations that may or may not relate in anyway to reality. For example CORs typically reduce with increasing velocity, but that's typically left out of games. I've seen game engines just take an unweighted average CORs of two impacting objects. A physically more realistic approach would be to do a weight the average of the CORs by the inverse of the stiffness of the objects.
Of course the COR and stiffness of each object depend not just on the material but the geometry. Even within a single object the location of the impact will change the COR and stiffness. A tuning fork, for example, has a very low stiffness on the outer tip of the fork, but a high stiffness on the joined end. To properly account for these variances one could do an FEA analysis on each object to create a COR and stiffness map that could be used by the physics engine.
However, unless realistic physics is important to the workings of the game, a single COR for each material type, and a weighted or unweighted average will probably be fun and look mostly realistic.