travel28- Yes, it is typically safe to use hair relaxers on children. However, you will not want to apply hair relaxers on children younger than 12. The texture of their hair is constantly changing and you risk damaging it by applying highly potent products such as hair relaxers.
Make sure that you do not apply the hair relaxer yourself. Attend your local salon and have a professional do it.
Also, even though hair relaxers are typically safe for children over 12 years of age, it would be a good idea to consult your child's doctor before using one. Some children can develop allergic reactions to some of the products in hair relaxers.