When the plugin manager is configured to use the "stable" update site, the users normally only receive notifications of new stable versions of Jenkins. The only problem is that the link to the changelog still points to the unstable releases, and even then the URL is not quite correct:
http://jenkins-ci.org/changelog.html
instead of:
http://jenkins-ci.org/changelog

The link for the stable changelog would be:
http://jenkins-ci.org/changelog-stable

The changelog is currently hardcoded in the hudson/model/UpdateCenter/CoreUpdateMonitor/message*.properties localization files, but it would be nice if that could be also a parameter provided to hudson/model/UpdateCenter/CoreUpdateMonitor/message.jelly

It appears that at the moment there is no easy way to figure out if currently a stable release is running, so potentially this could be added to the update-center.json's "core" object to make this feature possible.