I'm in the process of a child support case, can I pettition the courts to make my dead beat ex have mandatory visitation with his child?

No.

No, You can lead a horse to water but you can't make him drink. You can set up a schedule but you can't force him to adhere to it. Think about it. Do you really want your child to have a father that is forced to show up? How do you think that's going to work for the child?

No, you can force him to pay, force him to have his pay check garnished, but you can not force him to visit.

I never had any court orders of any kind but I would beg my x husband to spend time with HIS kids. It always turned out to be a drama and never ended up being a pleasant experience for my kids in the long run so it is better to not make an issue out of him seeing them.
If he can't see him from his heart it is a waste of time.

Seems pointless to force a guy to spend time with a kid if he doesn't already want to. What will that accomplish? Your ex will resent his child, and your child will see dad's disdain and resent his father. Let them come to terms with what their relationship will or will not be on their own. Focus on what you can be to your child instead, and leave dead-beat daddy in the dust.