Family Law Questions? Ask a Family Lawyer Online.
First, realize that although he is order to pay support - that doesn't automatically mean that he will get custody/visitation. The two issues are separate and distinctly different matters. It is considered every parent's duty and obligation to economically support their children.
So, with that being said, depending upon the history of the custody/visitation as between the parent and child (I would presume that there has been a relationship yet) usually a non-primary custodial parent eventually gets every other weekend, some vacation, alternating years as to Spring break, and alternating holidays.
It might take awhile for you to obtain that if there hasn't yet been a relationship as between the two fo them.