You could use a git filter driver which would, on checkout, take your README.md
(needed by GitHub) and generate a proper README
(needed by Python, although Lennart Regebro's answer suggests that PyPI does not require any README file)
So, keeping aside the fact that PyPI doesn't need a README (and the warning could be simply ignored), here is how you could (in general) generate the expected file with Git:

However, any modification to that private file README
would need to be reported manually to the README.md
file (at least because of markdown syntax which no script can guess for you)
That is why Noufal Ibrahim's answer (which I upvoted) might be more adapted, especially if you have access to symlinks (I am still with Windows Xp at work, so no luck for me):
Having make README
being a symlink to README.rst
, or, as Arto Bendiken comments:
=> having README.rst
being a symlink ro README
.
Git will store the symlink (and not the file the symlink refers to), so you can have both README
and its README.rst
file in your Git repo.