Recommend for warm story manga

You didn't mention any exclusively genre, so I am recommending this one - http://www.mangago.zone/read-manga/gakuen_babysitters/
Has all the things you are looking for ^^

http://www.mangago.zone/read-manga/love_so_life/

this one's cute http://www.mangago.zone/read-manga/kimi_ga_iru_basho/
you can check my http://www.mangago.zone/people/tag/49344/children/?page=1 more. it's a collection of cute kids in a BL manga that are relevant to the story.

I have several manga in my list which have a story about kids.. you can check them on this list : http://www.mangago.zone/home/mangalist/70782/

but I recommend you to read this :
http://www.mangago.zone/read-manga/love_so_life/
http://www.mangago.zone/read-manga/chichi_kogusa/
http://www.mangago.zone/read-manga/baby_kokoro_no_mama_ni/
http://www.mangago.zone/read-manga/beelzebub/
http://www.mangago.zone/read-manga/dangan_honey/
http://www.mangago.zone/read-manga/aishiteruze_baby/