Since you are not related to the children and not married to your BF, this would be taxed just like babysitting income if you were watching a strangers children.
If you are watching them in your home, you will need to use TurboTax Self-Employed to claim the income on Schedule C as a self-employed individual. You will need to pay self-employment taxes of 15.3% in addition to the federal, state and local income taxes. If you did watch them in your home, you would be able to deduct expenses you incurred to watch them, this would include mileage if you had to go to the school to pick them up or take them to practice or a Dr. appointment.
If you watched them in your BF's home, you would be considered a Nanny and your BF would need to treat you as an employee. This means he would need to issue you a W2 and pay half of your FICA (Social Security and Medicare Taxes) and withhold the other half from your pay.
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