No, there's no such greeting. In the last 150 years or so, a new era has been associated with the previous Emperor's demise, so it's not a happy event in the first place. This time is an exception, and people may be allowed to say something including , but there is no fixed, traditional way of saying congratulations.
(Disclaimer: I'm writing this from the standpoint of an ordinary native speaker. Experts may know some rare phrase that was used long ago.)