Every ticketed passenger--child or adult--is allowed one carry-on bag and one personal item, such as a briefcase, laptop case, purse or small backpack. So, if the child in question has a ticket (which is required if they are over two anyway), they can take the rolling suitcase (provided it meets the usual size requirements) and a backpack that fits under the seat in front of them. If the child is under two and travelling as a "lap child" without a ticket, they are not allowed any carry-on bags of their own.