There are rules about the way court documents can be served. One of the rules requires the person who served the documents to swear an Affidavit of Service. Affidavits of Service can only be sworn by adults. As a result, you cannot give the paperwork to a minor child to serve on another person.
Even if your child is at least 18 years old, you may not want to ask them to serve the documents. Many children do not like getting involved in issues between their parents.