The problem is that the site to be updated would have to be under Git to use the difference and have a proper .gitignore to keep the local files from being deleted.
Given those conditions, I think this might do it:
git diff v2.3.0-pl v2.3.1-pl > patch.diff
Then, after getting the git.diff file on the site, and assuming that 'git status' shows it up to date:
git apply --check patch.diff
Assuming that check shows no problems:
git apply --ignore-space-change --ignore-whitespace patch.diff
Does the version at GitHub still require a 'build" step before setup? That might keep this process from working.