In order to contribute to an IRA, you have to have earned income (either from self-employment or from wages).
I have assumed your child does not have taxable earned income and therefore would not qualify to contribute to an IRA.
You can, however speak to a financial advisor UGMA/UTMA accounts. Under the Uniform Gift to Minors Act or Uniform Transfer to Minors Act, you can open up custodial brokerage accounts for your kids. Although the account will initially be in your name, your child will be able to take full control of it once he or she reaches age 18 or 21, depending on state laws.
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