I made a test family and have found the following items increase the skills (ones not listed in game). Hope this helps!
Mental (Logic)
Fishing
Observatory
Play Game (Click on child they will play a game on cell phone - probably slowest way to level though)
Creative - Nothing new Learned but can be boosted the most
While child is on Activity Table select them with adult or teen and choose Encourage
If you have a teen/adult with a instrument maxed at 10 they can click the sim and choose mentor while they are playing. (Children can play Childs Violin and Piano)
Motor
Dancing
Social
Mirror (Practice Speech)
Just to add to that, once you max your kid skills, you can start on your adult skills, so if you max mental, you can start Logic and fishing.
Creative maxed, mostly gets you a good moodlet because you can max piano and violin as a child. Motor stays the same until you age up.
Social - Charisma can be learnt as a kid once social is maxed... in my test family the kid had her social skill maxed and was about to max the charisma skill, they showed up as separate items in the list of skills and charisma was maxed by the time the kid aged up.
While you are still a child you can get a start on comedy, writing, video gaming and programming, video gaming and programming a capped until you age up but writing and comedy can be maxed as a kid, writing through the computer and comedy through social interactions, the books won't work while still a kid.