Unfortunately, there is nothing you can do to force him to take the child at any point. Even if you go to Court, the Court and order a custody order based on what you agree to or what the Court feels is in the child's best interests but if the father doesn't want visitation, the Court will not force it upon him. You should consult with a family law attorney for some creative options.
One way that works to get some absent parents interested in more time is filing for child support. If he's not paying child support already, it might be time to go to court for that. Once he's paying child support, he might be more inclined to see his child more often. Of course, this can sometimes backfire and then all of a sudden, he's requesting joint or even full custody to lower child support obligations. Otherwise, I agree with the other attorney who say that there's not much you can do to force a parent to be involved in their child's life. Good luck!