Considered logically and grammatically, the irreverent utterance of exasperation should be for god’s sake, but it appears idiomatically in many other forms—for example:
He’s a third-stringer for God’s sakes! [The Collegian]
This is a school, for god sake, not a wilderness attraction! [LBPost]
They can’t even keep their hockey team, for god sakes, and Canada gets one? [The Star]
These are correct (and whether to capitalize god is up to each writer):
They were cartoons, for God’s sake. [Entertainment Weekly]
For God’s sake, let them parade and otherwise waste their time if they so choose! [New Vision]
See also for heaven’s sake and the sanitized version, for goodness’ sake (or for goodness’s sake, depending on your preference), which are likewise written many different ways.

