I am aware of Notify extension by Mercurial, but it always notify on any push action. What I want is that a notification only when a certain branch (say, "stable") is updated because I need others to take action when this happens.
What's the easiest way to achieve this functionality?
I think the simplest thing would be to extend the notify extension to do that (and add a new configuration choice). It should be quite simple (the hardest is to find the right ui so that we can add it upstream).
It's not a great workaround, but you could very easily write a hook that moves only changesets on stable over to a separate clone called (for example) email-trigger, and then have notify turned on there.
Or, have the emails go to an internal mailing list and set the spam filter on that list to throw away any emls without branch: stable in them, which will filter them away before the users see them.