I posted a solution to using git with bitbucket here:
http://forums.modx.com/thread/80939/git-workflow-on-modx-cloud#dis-post-454955
You could do the same thing with gitHub.
One thing I often do (and that is not in my post) is working directly on the files in the cloud by mounting the Cloud as a volume with Panic's Transmit and SFTP.
This is a bit slow, but great for small update to a live server or a Dev Cloud.
You can even work with SASS or a JavaScript minifier directly on the Cloud and then push everything to a remote git repo.