Is there an age to when a child is old enough to say I don't want to go with my noncustodial parent?

Generally speaking no. There is no set age upon which the court will allow the child to chose. They will however apply merit to the wishes of the child beginning around age 12 in some courts. As a general rule though the courts prefer to keep the children's exposure to the custody battle limited.

This Q&A was found on Children Need Both Parents : http://www.cnbpinc.org/modules/smartfaq/faq.php?faqid=69