First, the success of this endeavor depends as much on teaching the child to be calm and slower moving around the biddies as it does on the biddies. I mention this because some people have horrible luck with the best of biddies because their children run and shout. The thing to understand is that chickens have three main priorities: eating, not being eaten, and making more chickens. In other words, chickens aren't that different from some people.
My short list of breeds to consider:
Barred Rock
Orpingtons
Black Sex Link - usually a calmer, friendlier bird than the Red Sex Link
White Rock - look for a strain where laying is mentioned
California Gray
Delaware
Australorp
If eggs aren't a priority, consider bantam Cochins or Brahmas. They are charming and sociable.
To avoid:
Easter Eggers, sometimes mistakenly called Americanas - too variable in temperament
Leghorns - they literally bounce off the walls of the coop around active children
Cornish Cross - if not slaughtered, they tend to die of complications related to their aberrant physiology before the end of their first year - which causes needless trauma to children who have grown fond of them.
You will notice a theme here: calm British, Asian, and American birds. California Grays are exceptional in that they lay a white egg in contrast to the other birds in the list of good birds as backyard pets for children; they are a little higher strung, but calm down as they mature - and they are also very clever.
Silkies are often kept as pets; but they require very special care because of their feathers. Cochins and Brahmas require a dry area or they can have problems from their leg feathers being soaked.
Avoid roosters; some are sweethearts, others are vicious. I have known middle aged women who were terrified of chickens decades after their last encounter with a vicious rooster in early girlhood. The same for adult men, although they tend to not wish to admit it. On the other hand, I know of a little girl who carries her pet rooster around and dresses him in doll's clothing. He will lie down for a back and tummy rub, and loves to have her play with his feet. But avoiding roosters around small children is generally the safest way to go - more than one farm child has been blinded or disfigured by a bad rooster.
The safest way to have a peace in the coop is to select all the same breed, all the same color. This may not provide a great deal of visual variety, but it also tends to limit infighting if the birds must be spend most of their time in a run, even if each bird has twenty square feet in that run. Infighting not only causes problems between the chickens, it can make them nervous and difficult for people to approach as well.
We have a three year old Black Star who will die of natural causes if my husband and I have anything to say about it. Bird On Hand will climb onto our wrists for a "hand ride" if we lower an arm to her. We walk around the yard and hold her out to nibble on grape leaves, blueberries, etc. She received her name as a chick when we reached in to pick out chicks for gentle handling, and she would leap over and shove the others in order to jump into our hands - and she was not the dominant pullet in the brooder.
We have five yearling Dominiques who are very entertaining and active, but only enter laps if they receive a sufficient bribe. Their high activity level might make a child uncomfortable when biddy suddenly leaps several feet away in search of something she has just noticed. However, they will follow people about the yard in hopes of a treat or the people discovering something interesting to biddies.
