Only the court that set the current amount of child support can change it. But you most certainly can petition the court for a reduction in the amount. I see this quite frequently. For example, if you're durrently paying $700/mo in child support and can show with financial records that you can't meet your basic needs (food, shelter, clothing, transportation) then it's not at all uncommon for the court to reduce the amount you pay each month. The last thing the court wants is for you to lose your job because you can't meet your own basic needs. If that happens, then the court can rule any amount they want and you can't pay it. The courts know this. So if your petition for a reduction in payment amount is justified, rest assured the court will make the adjustment.
But *YOU* have to start this process.