Ok, I know suggestions come up about this and related topics occasionally. This is just my take on the general idea.
Have Playground or Daycare as an activity zone. It could work similar to hospitals in that you setup the zone, and there are just items you can add to it to increase it's benefits.
Item one: Toy bins.
Item two: Mini Workshops (there are *Dwarf* kids after all, slides and stuff are for elves.)
Item three: Caretakers.
Ok, basically the zone would work similar to a meeting zone, except adults would ignore it for the most part. Kids in the zone would get some happy thoughts plus gain a few skills depending on what is in the zone.
If nothing is in the zone, they would just gain some social skills.
If there are toy bins, they can gain a skill related to the toys they play with most. (Dabbling - Novice level).
The mini workshops would be basically a 2x2 workshop just like an adult workshop, but would not produce anything, and would allow the child to train up to a competent level of skill.
And having a Caretaker assigned who can work in the zone would have several benifits. (this could be added as a profession (Childcare)).
1. The kids could learn faster or better (could make it possible to gain another skill level).
2. The caretaker could clean up after the kids, or ensure they clean up after themselves. (Mainly putting toys back in bins).
3. They could swap toys for higher quality ones. Or replace broken toys.
etc...
Really the main idea I wanted to suggest was just setting it up as a zone.