First of all, I tried TheLQ's answer and even voted for that one (above), because it works for simple projects, especially if you also add wagon-scm and wagon-ssh dependencies to the maven-site-plugin and update all versions to the latest ;) With a multi-module project though I had an issue: each sub-module's site overwrites previously pushed content instead of nesting them (same problem with mvn deploy, i.e., deploying directly to a Hg managed remote maven repo does not create right folder hierarchy).
Therefore, here is an alternative solution, which also makes less commits to the remote repository (though, it requires a bit of manual work).
First, go to your Google Code project, https://code.google.com/p/MYPROJECT, tab "Administer", "Source" and create a new repository called, e.g., "site" (or how you'd like to call it). Then, you have to commit and push at least one file, conveniently called "index.html" to that repository.
Second, have the following in the parent project's pom.xml (only):
<distributionManagement>
<!-- ... other content ...-->
<site>
<id>MYPROJECT.googlecode.com</id>
<name>MYPROJECT auto-generated site</name>
<url>http://site.MYPROJECT.googlecode.com/hg</url>
</site>
</distributionManagement>
and also -
<url>http://site.MYPROJECT.googlecode.com/hg</url>
Note: Aye, it's "http:" and not "https:"; in my example, the URL is NOT going to be used by Maven to actually deploy the site content there (I am not going to execute site-deploy); instead, will use mvn site site:stage (see below). Also, you do not have to touch the settings.xml (the one in ~/.m2/ on *nix systems).
Third, simply clone the remote ('site') repository to your local machine (target directory can be under the parent project's dir as well as under anywhere else's - just cd to THAT_DIR where you want it):
cd THAT_DIR
hg clone https://USERNAME@code.google.com/p/MYPROJECT.site/
Note: if it existed, you do not have to clone again, just do hg pull, hg update (optionally remove old content using hg rm * and commit). You can also use e.g. free SourceTree software instead of console.
Next, from the projects root, do normally (skip 'clean, install' goals if you did already before; I used Maven 3.0.5):
mvn clean install site site:stage -DstagingDirectory=FullPathTo/MYPROJECT.site
Finally, switch to the clone/stage directory, THAT_DIR/MYPROJECT.site, test the website locally (open index.html in a browser), and if happy do:
hg add *
hg commit -m "re-generated MYPROJECT"
hg push
Check it out at http://site.MYREPO.googlecode.com/hg/index.html and the sources and changes at https://code.google.com/p/MYPROJECT.site/
Done.