Just keep in mind that essential oils should ne applied undiluted on child's skin and absolute no go is indigestion. Diffuse essential oils in aroma lamp, bowl with hot water or diffuser.
For child's sleep improvement use Lavender, Chamomille, Tangerine or Orange. You can use the same essential oils also in case of teething. If respiratory discomfort occures use Eukalyptus or Frankincense. You may also make a tummy massage with diluted Lavander oil (1drop) with any carrier oil (1 tablespoon) for colic relieve.