1099-MISC

As long as the parent reports the income you paid them on a tax return, you can take the dependent care credit on your tax return.   You will need to enter their SSN on your tax return and they need to claim the income as Self-Employment income on their tax return.    You do not need to give them a form, a parent is an exception to the general rule.   

• IRS Instructions Form 2441
• Form 2441
• How do I get the Child and Dependent Care in TurboTax?
• Where do I enter Schedule C?  (for the parent's return)

Where should the parent report this income on their return?

Miscellaneous income? 

They would need to report this as self-employed income. 

1. Go to federal>income and expenses>
2. Self-Employment>Self-employment income and expenses
3. Complete the profile that asks about your business
4. Then there will be a screen where you will enter your self-employment income.

@MLE8