If drafted correctly, a notarized agreement will act as a contract. A contract of this type would be enforceable. However, it would not be enforceable in the same ways as a child support order. An order is issued from a court and failure to follow it exposes the ordered party to pretty persuasive sanctions, such as contempt of court. Breach of a contract does not. Also, you’ll have to sue to enforce your contract, which takes time and money and creates all sorts of unnecessary heartache.
The better practice would be to go to court for a child support order. If you agree on the terms, you can stipulate to the agreed upon order, so long as it does not deprive that child of his or her right to support. Then, if the supporting parent decides not to pay, you have an actually enforceable order rather that a hollow promise with a notarized signature. An attorney can help you with this.
Best of luck to you.
This response is intended to be a general statement of law, should not be relied upon as legal advice, does not create an attorney/client relationship and does not create a right to continuing email exchanges.