You can contribute to a Roth IRA for him or her…up to $5,500 for 2018, but not more than the child’s earnings. Inside the Roth, earnings grow tax-free. The payin counts toward your $15,000 gift tax exclusion ($30,000 if married).
There are key tax benefits to Roths. All distributions made after age 59% are nontaxable. Contributions to Roths can be pulled out free of tax at any time. And when the child is ready to buy his or her first home, $10,000 of earnings can be taken out tax-free. See IRS Publications 590-A and 590-B for more details.