Most aromatherapy recipes and guidelines are intended for use on healthy adults who have consulted a medical professional. 

Essential oils used with children must be respected in the same way as over the counter drugs.  Most over the counter drugs will list different dosages depending on the child's weight and age.  Aromatherapy recipes that are meant for children should have significantly lower dosages of oils compared to an  adult blend.  

There are also many oils that should not be used on children.  For this reason you should stick to the oils that are generally consisted safe for use on children and only use them externally and for short periods of time.  Three oils that are consider safe for children are Lavender, Roman Chamomile and tree tea. 

There is an excellent resource book entitled Aromatherapy for the Healthy Child written by Valerie Ann Worwood.  This book contains over 300 pages of information and recipses for using oils on children.   It also suggest the amount of oil to be used depending on the  child's age, weight, health needs. 

Essential Oils can be beneficial to children if the the proper provisions are made.  So do your research, consult a medical professional and enjoy.