Procter & Gamble lists the following active ingredients in Vicks VapoRub: camphor (4.8 percent) menthol (2.6 percent) eucalyptus oil (1.2 percent)
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It also contains several inactive ingredients that may be responsible for some of its popular uses:

cedarleaf oil.
nutmeg oil.
petrolatum.
thymol.
turpentine oil.

You could try special nonmedicated rub for babies 3 months and older, called Baby rub.
This product contains fragrances and aloe in a petroleum jelly base but does not contain camphor oil. The blend is dubbed as a “soothing ointment” that contains fragrances of eucalyptus, rosemary, and lavender.