What to do with a 2-mo-old?
I wish I could remember where I read this, but I just came across something about games for that age. Apparently they really like textures--one game was just dropping a filmy scarf on them or letting them touch different textures. Also, dancing! I put my daughter in the Bjorn and dance around (although she does fall asleep).
From what I have read, just laying there and listening to sounds/ observing surroundings is enough stimulation for a newborn of that age. You do not want to overstimulate, as this will cause a lot of fussing/crying. I think just wearing the baby around is enough at this age. Maybe some soft singing, or humming, but thats about it. My babes are 4 months and all I do for stimulation is they have just started to grab at things so they lay under the play mat, they get tired of that after 10 mins, and I carry them around and talk to them softly. Sometimes we go outside and just sit, and they watch the things, in silence.
I think babywearing is enough stimulation both mentally and physically. The baby can see everything you are doing and can feel your skin, hair, the carrier etc... At around two months I wore both of my kids almost all day too. Sometimes I would tell them what i am doing, other times they'd just observe or listen to me singing along to the radio.