A Child's Right
Minor children are legally entitled to support from both parents, so child support technically belongs to your child, not to you. States take the view that you cannot waive something that was never yours. In some unique circumstances, such as if both you and your spouse earn extraordinarily high incomes, the court may allow you to avoid regular support payments, but not the support itself. For example, your spouse might set up a trust fund for your child that will provide for her in lieu of sending you a check every week.
Options to Using Payments
If you don't want or need your spouse's child support payments, you can set the money aside in an account for your child's use later; she might appreciate a nice windfall to sustain her when she graduates from college and is looking for a job. You might also decline to have your support payments go through your state's child support services, so there's no official record of whether your spouse is paying you. If he doesn't make regular payments, you don't have to legally pursue him for arrears. If you're collecting public assistance, however, it's usually mandatory that child support go through your state's collection services.