I have gone through a bunch of meta SE sites to see if they have any site promotion ideas that we hadn't though of yet. Here is what I found: 

* A leaflet, see e.g. the [leaflet for English Language & Usage](http://meta.english.stackexchange.com/questions/2155/english-se-pamphlet-hang-up-or-hand-out-to-your-friends-and-classmates). 
 * A leaflet like this may be used to promote the site at exhibitions (e.g. Expolangues in France, as mentioned on [ELL](http://meta.english.stackexchange.com/questions/2315/promoting-english-language-usage), or [Expolingua](http://www.expolingua.com/en/) in Berlin), in public libraries, adult education centres (e.g. Volkshochschulen in Germany), etc. 
* A subreddit, as proposed on [Linguistics SE](http://meta.linguistics.stackexchange.com/questions/326/sites-shutting-down-what-is-our-position). 
* A "Language learning flashmob week", like the [stats flashmob week](http://meta.stats.stackexchange.com/questions/341/how-to-promote-the-site) proposed on Cross Validated.
* "Polishing" the [questions with the highest number of views](http://languagelearning.stackexchange.com/questions/greatest-hits), as proposed on [French Language SE](http://meta.french.stackexchange.com/a/359/11052). 
* A question asking competition or question challenge week, as proposed on [Chinese Language SE](http://meta.chinese.stackexchange.com/questions/116/how-about-chinese-new-year-%E6%98%A5%E8%8A%82-question-challenge-week) (although there was [no response when the idea was repeated two years later](http://meta.chinese.stackexchange.com/questions/319/anyone-up-for-a-question-asking-competition)). The idea came from a StackOverflow blog post from 2012: [Hot Topics: A Contest Formula that Works](http://blog.stackoverflow.com/2012/01/hot-topics-a-contest-formula-that-works/). 
* Writing a great blogpost, as suggested on [Chess SE](http://meta.chess.stackexchange.com/a/108/10867). (This requires publication on a blog with a significant amount of traffic.)
* Creating our own blog, like [Worldbuilding SE's blog](https://medium.com/universe-factory) on Medium, as suggested by @fi12 in our [meta question about YouTube videos](http://meta.languagelearning.stackexchange.com/questions/337/should-we-create-a-youtube-account-to-promote-our-site).
* Retweeting upvoted questions on Twitter, as suggested on [Chess SE](http://meta.chess.stackexchange.com/a/108/10867). That is ... [if LL SE has a Twitter account](http://meta.languagelearning.stackexchange.com/questions/416/does-language-learning-se-have-a-twitter-account-and-if-yes-where-can-i-find-i). 

We can't do all of these things—let alone simultaneously—but we can do some of them, one after another.