You can really deduct any of your necessary expenses for conducting your babysitting. The IRS doesn't have a list because any expenses that are ordinary and necessary for you to conduct the child care are allowed as expenses.
With that being said, here are examples: house expenses (mortgage interest, property tax, utilities, house repairs, house insurance), furniture and appliances, household items (toilet paper, cleaning supplies etc. ) children's supplies ( arts crafts, toys) food expenses, car expenses if you need to drive the child.