Paper Moon Books in Punta Cana Village has a selection of books in English for hire.
We have a women's book club in Punta Cana that meets monthly and the members exchange books and have a stock of books - we just held a second-hand book sale for charity at the Christmas Bazaar on Saturday. You're welcome to join - about three of our members live in B?varo so you could share transport.
I've maintained my 3-book per week habit by supplementing all that with spending too much money on Amazon and more recently, buying a Kindle.