OS X: Git with client certificates rejected
It looks like you are facing the same problem as in this docker issue where they conclude it's likely a bug in OSX curl.
In some other post they suggest, that this could be caused by certificate serial number either being 1 or being too large to fit in 32 bits.
On your OS X 10.9 case, I think "Invalid Certificate" should be solved by adding the certificate to system key chain as trusted (discussed in this question).
This post describes some changes in OS X curl, which seem to be related. In my understanding, it might be solution to switch to different curl implementation (but likely that only could work if git would also be installed using brew).
As Michal already mentioned it is a OSX curl bug. A possible solution would be to install a git version which does not rely the osx curl implementation
- Install macports: https://www.macports.org/install.php
- $port -v selfupdate
- $port install git