If your child's other parent is ignoring court-ordered child support payments, don't let them get away with it, even if you can manage without them. Report them to the court. Although the system tends to move slowly, child support law requires them to track the culprit down and force payment.
In the event that the system fails you, child support law does allow you to go after a deadbeat parent on your own. You'll need a capable and experienced lawyer who specializes in child support, and unless you can recover legal fees from the deadbeat, expect the process to be costly.