You will claim your rent as a "Business Use of Home" expense. In TurboTax Self-Employed you will be asked; 

" Did you use a part of your home for work?". Answer Yes to this question and then continue through to add the information of the square footage and hours/days your home is used for daycare purposes. Then you will see some spaces that say "Other Expenses" and you can type in "Rent" and the total amount you paid for rent in the year.