Just a word up-front: Children’s stories does not necessarily mean “easier language” as children are of course able to speak normal Japanese, but it often means “less kanji” which makes it even harder for WK members 
(but is good practice anyways).
Having said that, have you looked at the Beginner Book Club book picks?
魔女の宅急便 (Kiki's Delivery Service) Home Thread - Beginner's Book Club and its repeat club 魔女の宅急便・Kiki's Delivery Service 🧧 Repeat Club is a classic around here - it’s slice-of-life and coming-of-age of a young witch. I thought it’s very cute. Some beginners complain that the language is a bit flowery, but I guess that is Japanese for you.
時をかける少女 Home Thread (Beginner Book Club) is proper time-travel SciFi, the author is well-known, although the pacing of the story was not to everybody’s liking (way too slow then way too fast). If you can live with that, it’s an interesting story, I thought.
霧のむこうのふしぎな町 ・ Mysterious Town Beyond the Mist (BBC) 🌬 🏘 is also about a child; she is spending her summer holidays in an unusual location (with some fantasy elements) and grows a lot. The first chapter contains a fair bit of Tohoku dialect, which killed some readers, but otherwise I found it to be pretty readable.
小川未明童話集 - Ogawa Mimei’s Collection of Children’s Stories (Beginner Book Club) is a pretty old collection of children’s stories. They are quite interesting from a cultural aspect, but most of them are not at all what you would expect, they are either pretty strange in itself or have a strange ending, mostly. The good thing is that they are independent of each other so you can jump in and out as you please. Most of them are also available on Aozora for free.
We also read this book as a group:
狐笛のかなた (Koteki no Kanata) Home Thread It’s solid fantasy (as in “medieval setting”), the protagonist is a young girl who has to face the evil of the world, let’s say. The author is well-known for her complex world building and long stories, and I like her a lot, but this one is luckily shorter and aimed towards younger readers, so the world building is not as complex and long-winding. I did not like it as much as the other books as it was a bit too simplistic and predictable, I thought, but definitely a good beginner’s book nonetheless.
Oh and then there is one of my personal favorites, おおかみこどもの雨と雪 - a coming-of-age of a young mother and her two very unusual (and very different) children. It’s a bit longer, so it’s a bit of an investment, but I found the language to be very accessible once you get used to the writing style (tons of compound verbs, for example).
There are also some Intermediate Club books that are on the easier side, like Konbini Ningen, but for the moment I did not look at suggesting something from that club. I can always add more if you like 