I would also explain to her that the deduction she might get for what she pays you will likely be far less than what she is SAVING by not paying center rates. If you are giving her a $50/week break over center rates, and you watch the child say 50 weeks out of the year, she's getting a $2500/year savings, would she get more than that if she claimed the expense?
I would at the very least look into what the licensing regulations are for your state, just to see whether it would be worthwhile to pursue that avenue. Some states don't require licensing until you hit a certain # of children. Licensing really has nothing to do with whether you choose to claim the income or not, IRS could care less about licensing.
If you do claim this income on your tax return you'll at minimum have to file a Schedule C (self employment income) and Schedule SE (self employment tax). If you choose to write off expenses related to your home (mortgage interest, property tax, electric and utilities) you will have to refer to this IRS publication:
http://www.irs.gov/pub/irs-pdf/p587.pdf
This deduction is calculated on a "time-space" percentage. You will also have to add a form 8829 if you choose to do this.
At the end of the tax year, you would need to provide her with a Form W10 with your SSN:
http://www.irs.gov/pub/irs-pdf/fw10.pdf
One thing I hope you've thought about and would REALLY like to stress is that whether you are licensed, unlicensed, paid under the table or "above board", please make sure you have a written and signed contract spelling out ALL the details of this childcare arrangement (hours, pay, scheduled days off, etc.). There are far too many times I've seen and heard of people being taken advantage of in "informal" childcare arrangements.