My son is 19 and His girlfriend is 16, he is wondering if he has any rights more to his child than his girlfriends parents?

Depends on where he lives at this time. Having a child with a 16 year old may or may not be legal in the state that he lives in. His best interest would be to go to court and establish paternity. And try to get set up on a regular visitation and child support schedule.

ANY question on law needs to include your general locale as laws vary by area.

As noted, your son may be subject to prosecution for statutory rape. That may be a bigger concern.

If that is not a factor, then once the child is born, he can apply for joint custody and visitation. The mother will probably then file for child support. Until the child is born he has no rights.