Although there can be no instance where the court will allow that the non-custodial parent is not required to pay any child support, there is a matter of whether or not the custodial parent will collect, or enforce, these payments. In some instances, the court will not always know that a parent is not making custody payments unless the spouse that should be receiving said payments reports that they haven’t received any support. Beyond that, if the custodial parent does not feel like reporting the lack of payments coming in, then the non-paying parent is not likely to face any serious problems.
The reason that a court does not allow for no payments to be made is not actually about the parents, but rather the child. It is the child that is legally entitled to receive these payments (as that is who these payments are intended to benefit), up until they are 18. The most common way that child support orders come about is as part of a divorce process, along with the custody order. An example of this would be when the court is deciding which parent the child will spend the majority of time with, the next logical step would be figuring out how much the non-custodial parent will be paying in child support.
The other instance in which a child support order comes about is if the parents are not married, and the parent who the child resides with seeks some type of support. Although this can only begin after paternity has been established for both parents, herein lies the situation in which a parent is not paying child support without court enforcement. If the parents decide that the parent not living with the child does not need to pay support, as they are going to leave the child’s life or the support is not needed, and they never go to court about the issue, then in this situation, yes, you can agree amongst yourselves that there need not be any child support.