Maybe an acoustic that can be plugged in? Not sure if this is the size you're looking at, but the Martin LX1 is like a 3/4 size guitar (23" scale) that comes with a plug in version. I used to use one as a desk guitar, but recently got a slightly larger dread. jr. with 24" scale. I would recommend at least something that sort of stays in tune, or else the kid might get bored really fast.