“Της κυβέρνησης” και “της κυβερνήσεως” are both correct.
The modern Greek ending is the ης.
The ending εως is ancient Greek. It has survived till nowadays, however it is much more formal.
We can find the ending εως in formal documents like “εφημερίδα της κυβερνήσεως” or we can hear it in a formal conversation ( for example between politicians).