I just got an email from Audible and it seems from stories.audible.com there are several free stories “for kids” in Japanese among other languages. I will definitely be giving it a shot later!
Thanks.
Are they just Audio or are there scripts we can use to follow along?
I don’t see any scripts, but I listened to 赤いろうそくと人魚 and it’s read slowly with very soothing classical music.
Title is a bit click-baity 
Furthermore, there are at least three threads about the same thing…