I suggest editing MediaWiki:Tagline and putting the "beta" there. That might be done for any Wikinews editions which does not yet have a sufficient level of activity. This is better than defacing the logo, in my opinion.
It turns out that it is very difficult to predict that activity, and I don't think the current process on Meta is really anywhere close to doing that. The Swedish Wikinews is very active, for example, thanks in large part to a handful of dedicated editors -- but that might change any day. Of course, all the editions are suffering from the current slowness, and recent downtime.
One notable difference in Wikinews to other projects is that a quick glance at the frontpage gives you an impression of the level of activity: if you only see old news, obviously the project is not very active. This is good if it is seen as an incentive to work on it, bad if it frustrates people and makes them give up on the project. Wikipedia, Wikibooks, Wikisource, Wiktionary in the different languages all have their phases of activity and inactivity, but nowhere are those phases more visible than on Wikinews.
Switching the project into read-only whenever it enters such a phase seems like a bad and un-wiki idea; perhaps you could create a template like this for the frontpage instead:
The French edition of Wikinews is currently not very active. Please participate in building this website into a useful resource! Ideas for increasing activity are collected at [[Wikinews:Building Wikinews]].
Here are a few suggestions to increase activity:
1) Translate. It is much easier to translate a well-written article than to write a new one from scratch. Wikinews articles have to grow to publishable quality very fast, "stubs" aren't helpful, and references are a strict requirement. As such, writing them takes a lot of effort. But the English Wikinews, for example, is now publishing articles at a reasonable rate. As an author of that edition, I also get great satisfaction out of knowing that my work is going to be translated into languages I do not speak.
2) Prominently link the equivalent of http://en.wikinews.org/wiki/Wikinews:Submit_a_story - this helps to attract people who do not know about the Wikinews process and just want to get their feet wet.
3) Have brief news items on the frontpage which aren't fully developed stories yet. This should only be done until real stories are being published regularly, so as to not conflict with the [[Current events]] pages on Wikipedia.
4) Edit MediaWiki:Sitenotice and point people to the IRC channel, mailing list and Village Pump. Building a community helps to create a feeling of identity and the desire to protect that community, which is an incentive to do work on the site.
5) Organize and participate in events like the design contest or the Wikinews chats. Point people on Wikipedia to these events to get them interested in the project.
6) If you are a software developer, help us to implement MediaWiki features like category RSS feeds and dynamic article display. http://bugzilla.wikimedia.org/show_bug.cgi?id=1411 is the only code currently being actively worked on, to my knowledge.
Please also join the international Wikinews channel at #wikinews -- a lot of good people are hanging out there who may help you to answer questions with the project.
Regards,
Erik