Yep, set up your own private league and just switch the settings to be as simple as possible.
I haven't tried it, but I don't see why you couldn't go so far as to set up a 6 person roto league with only 4 simple categories (say, HR/AVG and W/ERA) and only 15 roster spots (C/1/2/3/S/OF/OF/OF/P/P/P/P/BN/BN/BN). Set it up for weekly moves.
You could even do the draft off-line in the comfort of your own living room and manually put in the players later. I don't think you'd have any problem at all.
Unfortunately, my son is only 2, so I won't be able to do this with him this year. Maybe next year.