Where can I buy online cheap children's story books?

You should check out Lazada! I bought one for my younger sister last week! and she just loves stories being read to her. http://www.lazada.com.ph/shop-local-children-books/

If second hand books are just fine for you, you may join groups for bookworms like Awesome Book Swap. There, lots of story books for kids are available

National Bookstore delivers! You may check their website to search for book titles, add it in your cart and have it delivered right at your door step.

Booksale has kiddie books ranging from 5 - 50 pesos. Most of the malls have Booksale Bookstore.