This is such a good question.

He was definitely either born one, or he was made one, but I think because of the way he likes to bite children, he was probably born one. For one thing, if he was born a Werewolf, he wouldn't have had the chance at a normal childhood. It would have been pretty much plagued with A) no friends, B) Perhaps neglect or his parents horrified by him/hating him C) Would therefore, in an act of revenge and bitterness, want other children to suffer like he had. Greyback obviously loves biting the children, so there's always the possibility he was bitten, but it seems a little more.. deep from what he does that I assume he was born one.