Try restoring the monarchy. There are at least two Romanov pretenders -- pick one and install him. That will put a gloss of conservative legitimacy on your coup. Of course, in the process, you can make the monarchy as constitutional as you like -- the new Tsar might reign but not rule.
Consider the example of Spain. King Juan Carlos provided the stability necessary for his country to transition from fascism to democracy.
Consider the example of Spain. King Juan Carlos provided the stability necessary for his country to transition from fascism to democracy.