I do not understand what you are talking about. Children go through naturalization like everybody else. They have separate paperwork that their parents fill out for them. Obviously they do not swear oaths or do tests, but they get their own citizenship documents that are legally separate entities from their parents. A parent can have a green card or citizenship while the child does not and vice versa.
http://www.immigrationdirect.com/greencard/Green-Card-for-Child.jsp?gclid=CKa48vTqwboCFQVBQgodPQQAeQ
A green card is not citizenship.