Most often this is achieved by the parties agreeing to "hold open" child support based on the parenting time and expenses incurred by both parties for the support of the child(ren). This is common in situations where the father of the child is living with the child’s mother, they are not married, and neither party wants to establish child support.
A "hold open" on child support requires neither party to pay support, but makes child support available should there be a change in placement or economic circumstances of the parties. To change child support from being held open, a party would need to file a motion with the court and request a change in child support.
In general, if the parties have a current child support order and wish to stop the support obligation pursuant to an agreement, it would be necessary for the parties to execute an agreement and file it with the court along with a motion to modify the child support.
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Depending on the jurisdiction, the court would either approve the agreement and incorporate it into an order, or the court would hold a hearing and decide whether to approve the agreement and incorporate into an order.
Due to the variances in state laws, it is recommended that you consult with an attorney licensed in your state to review your case and provide you with legal advice on your current options.