Amazon is a little late to the (non-food) subscription box fad, but that won't stop it from shipping children's books to your door. Prime Book Box Kids is targeted at parents, and will deliver either a pair of hardcover books or a quartet of board books on a regular basis. There are four age ranges to choose from, with appropriate titles available for infants all the way up to tweens.
You get to choose the frequency of deliveries (monthly, every other or quarterly), and the titles are checked against your purchase history to help prevent duplicates. Before each delivery you'l get an email previewing what's in the box, and if you aren't a fan of the pre-selected books there will be four alternates. And, if you don't like any of those, you can skip the order entirely.
It's probably a lot smarter doing this with hardbound titles and board books for kids than it would be shipping them kid-friendly Kindle books the way Amazon does for adults. Plus, everyone likes getting a box from Amazon with their name on it, and kids are no different. Of course, if you're looking to keep your budget low, you could achieve pretty much the same thing by taking your little ones to the library at regular intervals.
Actual pricing isn't entirely clear, but the FAQ page gives a clue. "Prime Book Box saves you up to 35 percent off list price, and is always an equal or better value than Amazon's everyday low prices. In the event that the books in your box are available from Amazon.com for less than $22.99 at the time your order is placed, you'll receive the lower price automatically," one section reads. The program is invite-only for now, and you can request an invitation at the source link below.