If the only income from the business is from mom and dad, that could be a problem. If junior has 8 or 10 customers and is mowing those yards, that would work just fine. You also could run into problems if the parent is paying an unreasonably high amount to the child (so that the full IRA could be funded) relative to the others.GE said:
www.fidelity.com/retirement-ira/roth-ira-kids
According to Fidelity, earned income for the child can come from a job or self-employment. The examples given are mowing lawns, babysitting, and shovelling snow. I'm not advocating lying to the IRS so don't just say they did these things and contribute for them, but if they do legitimate work of this nature there is no reason you can't contribute for them up to their qualifying earnings.
The kid would have to file a tax return and would owe self-employment tax. The amount used to determine Junior's IRA contribution is the net profit from the business, not the gross. Junior, if in Texas, would also have to file and pay sales tax on the work he does and if he owns any of his own equipment would have to render the personal property to the appraisal district.
All of this can work but it isn't quite as cut and dried as has been presented. It works much better when the parents, or an aunt or uncle, or some family member has a business and is willing to hire the kid.