Massaging your baby is a wonderful way to bond and provide your baby with a pleasurable form of stimulation that will enhance your baby's overall development. Massage has a profound impact on the brain's development and therefore paves the way for your child to best achieve his/her potential.

Guidelines for Dilution (from Tisserand's Essential Oil Safety, 2nd Edition, page 47)
Premature - we don't suggest using essential oils until more mature
Newborn - 3 months | 0.1% - 0.2% / 1-2 drops per ounce carrier
3 - 24 months  | .25% - .50% / 2-6 drops per ounce carrier
2 - 6 years | 1% - 2.5% / 8-23 drops per ounce of carrier
6 - 14 years | 1.5% - 3+% / 12-28 drops per ounce of carrier
Hot oils such as Oregano or Cinnamon | 0.07% / 1 drop per 2 ounces carrier

Popular Essential Oils for Baby Massage
Cedarwood Atlas - may promote deep sleep, good for the skin
Geranium - relaxing and good for the skin
German Chamomile - good for the skin, supports digestion, dark blue and strong aroma
Lavender - good for skin and well known for its ability to help alleviate stress
Mandarin - calming, supports digestion (unlike many citrus oils, it is not phototoxic)
Palmarosa - calming, supports digestion
Roman Chamomile - calming and relaxing, good for skin, has been used for teething
Sleepy Time Moisturizing Spray (12 drops per ounce - use with caution for children under 2 years of age)
Tender Skin Moisturizing Spray (12 drops per ounce)
Mother's Moisturizing Spray (25 drops per ounce - use with caution for children under 2 years of age)
Peaceful Moisturizing Spray (25 drops per ounce - use with caution for children under 2 years of age)

Popular Vegetable Oils for Baby Massage
Almond
Avocado
Coconut oil
Grapeseed
Meadowfoam
Pomegranate

Benefits for Baby
•    Promotes bonding and communication
•    Assists in overall growth and development
•    Promotes sounder and longer sleep
•    Improves function of the respiratory, circulatory, digestive, eliminative, nervous, and immune systems
•    Reduces the symptoms of colic, gas and GI tract distress
•    Gives relief from the discomfort of teething and congestion
•    Improves sensory awareness
•    Helps baby learn to relax, decreases production of stress hormones
•    Reduces fussiness
•    Enhances awareness of being loved, accepted, and responded to
•    Assists in increased vocalizations

Other Benefits
•    Cross cultural studies show that babies who are held, massaged, carried, rocked and breastfed, grow into adults that are less aggressive and violent, and are more compassionate and cooperative
•    Recent research shows benefits for children with asthma, diabetes, and premature infants
•    Mothers with postpartum depression have shown improvement after starting infant massage

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References
Tisserand, Robert; Young, Rodney, Essential Oil Safety: A Guide for Health Care Professionals, Elsevier Health Sciences UK 2nd Edition 2014, page 47.
Worwood, Valerie, Aromatherapy for the Healthy Child, 2000, pages 34-35.