I'm not a CPA or even a financial advisor, and you have to find your comfort zone with this. Here's my opinion based on what I've read and what we've done. The IRS has never shown any interest in us.
The key to starting a child's Roth IRA is showing that the earned income is credible.
A toddler could easily earn money as a photo model. A nine-year-old could easily have a dog-walking business. A 12-year-old could be a blogger or a website programmer or a lawn-mowing entrepreneur. All of them could get paid for household chores, although arguably the 12-year-old would earn more than a toddler. If the toddler ends up on the cover of Parents magazine, though, then their income is totally credible because it's documented by a business on a 1099.
The IRS does not publicize their flags for tax returns, but the tax court decisions give some insights. The IRS is not going to waste their time auditing your 9-year-old's $1000 Roth IRA unless they already suspected major fraud elsewhere-- or happened to be doing one of their infamous random "lifestyle audits" on everything in your family's tax returns. The IRS auditor would rather go after millionaires than minors, and your worst case would possibly be a letter generated by a computer program. Even then your written response would stick to your guns on your children's earned income for household chores or entrepreneurial businesses, and the IRS would stop asking questions.
I documented our daughter's family earned income in Quicken. It started with household chores and steadily escalated to yardwork, helping maintain our rental property, car washing & oil changes, and neighborhood childcare. When she got a part-time job at a tutoring service she had W-2s. Sometimes her boss would pay her a cash bonus (probably under the table and undeclared) and we'd note that in Quicken. I even paid her to run errands and to help me with the blog.
You only have to file a tax return if their earned income is over a threshold. (There's a flowchart for "Do I have to file a tax return?") When their W-2 income is reduced by federal and state tax withholding deductions, then you have to file a tax return to get that refunded. There's no requirement to file a tax return just for contributing to a Roth IRA. The nice thing about filing a tax return anyway is that you formally declare the family chores as earned income (even if it's not enough to pay taxes) so that the IRS knows you're not hiding anything.
At tax time, we'd sit down with her W-2s (and in college, with her 1099s) and our Quicken records. We'd make sure that she could document earned income up to the Roth IRA contribution limit. She'd enter in the W-2 and 1099s into the tax software and then declare her additional income up to the contribution limit. (On Turbotax it's way down at the bottom of the income menu, something like "earned income for which you have no W-2" or "earned income as a family member".) For example, one year she'd earn $3500 from W-2/1099 income and $2000 from family chores/jobs. She'd enter the $3500 as part of the W-2/1099 data forms, and then she'd declare the other $2000 of family earned income so that she could declare the Roth IRA contribution limit of $5500. Another year she had "only" $2500 of W-2 income and $2000 of family chores/jobs, so she could only declare a Roth IRA contribution of $4500. That gave her an incentive to seek out more work or more chores for more family earned income. Then in Turbotax she'd declare the Roth IRA contribution. Her tax filer's standard deduction usually meant no federal tax, and she rarely owed more than a few bucks of Hawaii state tax.
You can't declare money saved from previous years. IRA contributions for a tax year can be made from 1 January of the current year through 15 April of the following year, but the earned income for that contribution has to be earned from 1 January-31 December.
Gifts from birthdays or other holidays are not earned income. Money for grades is a hotly-debated subject because the teacher and the school assign the grades but they're not paying the money, so arguably children are just getting a gift from you for turning in a good report card. If you were homeschooling your children (and paying them for homeschool labor) then you might have a labor-for-hire situation.
You could also pay children for other learning outside of school, like auto maintenance or home repairs. I used to pay my daughter $10 for car washes but $15/hour for replacing a toilet or doing electrical work. I told her that was because she had to have more skills, more safety, and work longer for the bigger jobs. My parental reason was to motivate her to learn plumbing and electrical skills.
She was mightily annoyed to learn that neighbors paid me $35/hour to fix their toilets and wire their receptacles, but I told her that was because I have more skills & experience than her. Well, she showed me-- she got her degree in civil engineering.
Unless you are planning to employ your children, with all the taxes associated with a business, no you cannot do what you are planning.
I agree that gifts are not earned income.
I don't know all the state laws, but paying a kid for doing jobs around the house does not require paying business taxes in Hawaii. Paying a kid for doing chores on your rental property could hypothetically be a Schedule E deduction, although everyone has to find their comfort zone with that-- especially if you pay a contractor kid $600 or more per year and get into 1099 territory. Paying a kid for helping with your blog could be another deduction, and the blog income would probably be subject to tax as self-employment income. Getting your kid's headshot on the cover of Parents magazine would be a straight 1099 earned income situation, and the kid would pay the income taxes (if any) on that. A college student on work-study (campus tours, alumni fundraising call center) could easily earn more than $5500/year, although you'd have to use the college's 1099 and 1098 forms to report some of that income. A college student on a NROTC scholarship receives a monthly stipend, but a service academy student receives their money as monthly earned income.
It gets messy. Pub 15 and Pub 590 cover almost every situation, but you might have to check with a tax professional for your state & locality tax laws.
