I don’t know of a Corona specific way, however, what we do is have our main Serenity framework ( at Glitch ) and my own personal Puggle library set up as repos on BitBucket, then when we create a new game we naturally have that setup as a bitbucket repo as well.
We can then easily add those frameworks as submodules to our games, allowing the latest code to get pulled from the individual repos and any changes we make in the game repo can then get pushed back to the library repos ready for all other games that use them ( hopefully that makes some kind of sense? )
When we want to pull down the serenity framework into our new game, we just use this command:
git submodule add https://bitbucket.org/path/to/repo serenity
A bit more info about submodules can be read here - http://blogs.atlassian.com/2011/12/git-submodules/
Please note though, I am by no means a Git expert. All I know is that this works for us. There are possibly other ( probably better ) ways to do this, but this works.