I have three "Book of the month club" accounts--they are the same root club, but I have three accounts to maintain (membership fulfillment, done, Featured Selection cancellations--still have to send some more back that I forgot about). I am with the Children's Book of the Month Club, Homestyle Books, and Rhapsody Book Club (yes, romance novels, my deeply secret sick or bad pregnant day indulgence). I haven't had bad experiences with those so far. I like that with the Children's book club you often get shipping for $2.49 for purchases of $25. They have a decent variety of books and the copies are good quality. I have gotten a lot of gift books that way. I am indifferent to the Homestyle book club but have sadly gotten to enjoy romance novels a bit and enjoy getting those on good sales, too.
Now, that said (or rather written), I'm not sure if that is what you mean. If you are asking about something where a child gets a specific book every month like a magazine, I have no idea. You could do a kids' magazine subscription, such as Highlights, Babybug, or the kids' versions of National Geographic and the like. Those tend to be pretty good.