Make sure you have SSH keys for Github (or Gitlab) setup so that you can do this from a command line
git clone git@github.com:scottellis/private-repo.git
Then your Google Repo manifest xml can have a remote entry for the private repository that looks like this.
<?xml version="1.0" encoding="UTF-8"?>
<manifest>
<remote name="github-public" fetch="git://github.com"/>
<remote name="github-private" fetch="ssh://git@github.com"/>
<project name="scottellis/tspress" remote="github-public" revision="master"/>
<project name="scottellis/zmon" remote="github-private" revision="master"/>
</manifest>