I don’t know if this existed at the time this thread was originally posted, but looks like setting up an organization on http://hex.pm is going to be the cleanest way to do this. You could deploy your own self-hosted version of the hex.pm app but it seems that this is ultimately going to be the easiest way to get going out of the box that still permits full resolution dependency, and without having to personally maintain an external/private hex.pm service.
Remember that with git you can access individual private repositories from a github account, but as @josevalim mentioned mix will not perform dependency resolution on those apps and you may end up with conflicts, and possibly having to maintain the dependencies for your private elixir libraries in the top-level app in which they’re being used. This might work for a very simple application but breaks and is clumsy to maintain at scale.
If you don’t want to use hex.pm organizations for whatever reason I’m sure you could also configure this on your own server, though the setup overhead will be more involved. I get the sense too that hex.pm organizations will become an increasingly common workflow in Elixir projects, and will be easier to onboard other developers already familiar with that relatively straightforward process.
