Child support is based on a number of factors. One of which is the gross income of the parties. If one can't prove their income because they are paid in cash, then their income will be imputed (assumed) at a rate set by the state. They could then be ordered to pay the other parent directly or through the state system. Either way, if they fail to pay they can be held in contempt (if their failure was willful). You would be best served by talking to a lawyer.
Family law attorneys in these situations occasionally employ private detectives to discover and document wrongdoing by the other party. This can definitely be done if someone who owes child support is hiding income. If there is already an order is place then payments must be made by the obligor according to that order.
From your question, it sounds as if there is already an order in place. If so, then your options are limited to a contempt proceeding. If money were not an object, hiring a private investigator would be an option, but not one I would usually recommend where money is tight.
Often, courts can hold the person in contempt and require the full back amount due be paid before they are released, some other amount or the court can freeze any bank accounts with his/her name or social security attached.
Your local county should have a child support office which might provide free legal assistance. You would be better served by having an attorney with you.