If there has already been a judgement for child support in the past, can I go back and amend to receive 50/50 custody with no child support?

If there has been a change in the circumstances of the children and modifying the prior orders would be in the best interest of the child(ren), then the court can change the custody agreement and award 50/50 custody... and potentially waive child support.   The modification, however, will not be retroactive... meaning your stuck with what you owe until the new order is signed.  It won't undo any other deliquent or accrued obligations. 

The second part of your question inquires about the success of a modification.  The courts don't like to see parents in every year tweaking the orders, but they do allow modifications whenever it's in the best interest of the child.  In family law, final orders are rarely ever final.  The success of your motion will depend on the factors of your household and your request.  Factors the court can look at include:  the desire of the children to live with you part-time, a deterioration of the household of the other parent (physically, financially, or emotionally),  misconduct by the other parent, a change in the circumstances of the child.  This is not an exhaustive list, but it does give you an idea of what the court is going to look at when deciding whether or not go give you 50/50 custody.

No attorney can ethically guarantee you a result.  But if you have some information noted above which demonstrates that a change would be good for the child(ren), then each additional piece of evidence will improve your chances.  Many family law attorneys do conduct free or cheap consultations.  You may want to visit with several family law attorneys in your area to get a better feel of the facts of your case and how your judge has historically dealt with the custody issues.