If you put a git repository in a shared drive via git clone --bare (makes it not checkout a branch, and doesn't setup any origin type stuff), you can use that as a remote, pushing/pulling etc. Setting up a network available shared drive on one of the two computers shouldn't be too difficult, and by git's distributed nature it's not exactly the end of the world if access temporary.

Another option would be to use the email-based workflow, but that's quite different from most people's expected git experience.