The child will have to file a tax return and show income from self employment on Schedule C to count as earned income.
They (or you) can only contribute to a IRA up to the 6500 max or the Schedule C net profit reduced by the deduction allowed for the ER portion of your self-employment taxes whichever is less. See IRS publication 590A (page 39 for ROTH) https://www.irs.gov/pub/irs-pdf/p590a.pdf
