Any parent can execute a voluntary relinquishment of parental rights. This form is widely available on the internet but must contain certain language to be approved by the court. The execution of the voluntary relinquishment of parental rights does not terminate child support. In order to terminate child support an order must be entered and approved by the court. Often, courts will approve a relinquishment provided its in the best interest of the child and not merely to avoid a financial obligation.
Any answer or response to your question I may provide does not establish or constitute an attorney-client relationship and is for general informational purposes only.
A voluntary termination must be approved by the judge. A termination of rights ends the child support obligation. A parent entitled to receive child support may waive accrued unpaid child support unless she has received state aid for the child. In that event, it's the State's money.
I am not intending this to be legal advice, because I don't know the particulars of your situation. Call me if you would like to discuss this or other isues.