Pitbulls are protective and aim to please.

Pitbull
Because so many have been abused and taken advantage of for their fierce loyalty and muscular bodies, pitbulls have complicated reputations and can invoke fear.  But they can be wonderful dogs with children.

Like other strong and protective breeds, they should be monitored with children. And sadly, many pitbulls who wind up in shelters because of abusive situations may not have patience for children because of their past.
But their personalities are generally gentle and aim to please. If you make it clear their job is to protect and play with the baby, a pitbull can do it flawlessly.