Unstoppable, rotting corpse Jason Voorhees is essentially nothing more than a mindless killer. His one-track mind and distinct lack of anything resembling an intelligence would render him unable to use most of the other rings (not that he has the emotional capacity to wield them anyway). But can you really imagine him trying to master flight and construct creation?
Fortunately, the Black Lantern rings tend to provide the wielder with a completely different personality to the one they're familiar with and, rather than the complex intricacies of the other rings, the power-focus is on regeneration and super-strength more than anything else.
This would suit Jason down to the ground and would make him a mass-murdering force to be reckoned with.