Well, we made an app for Android called:
$1The original intent was for it to be the blind man's drawing tool - where they could draw with finger, and then feel what they have drawn.
This arose out of some discussions we were having in the eyes-free google group (which is a group for blind and visually impaired android users - we were there because we interact with them to get one of our audio recorder apps to be accessible for blind users as well - since it is designed to be used for heads-up use).
Anyway, with all that context out of the way, the app itself does not in practice work that well. The problem is that we used vibration of the phones to simulate the buzz you feel when your fingerprints moves ridge by ridge over a texture.
That was the intention - to make a phone give the sense of haptic feedback or tactile feedback similar to swiping your finger over a piece of paper or a textured surface.
In practice it doesn't work that well, because phone vibration modules are not that responsive, and are usually just oscillators.
HOWEVER, there is potential if we were to use audio feedback, where the audio were to mimic the sense you get from feeling a textured surface - well like a phonograph needle moving over a textured surface type of thing - that could be done. But android's audio latency is not so great (compared to iphone). So it remains to be seen how perfect that could be made.
But we had several users on the eyes-free google group test it out, and some of them reported they were able to write simple letters and recognize them by feeling.
Later we also got feedback that one of the users there had used it to instruct blind children - i.e. had them draw things, and then used an embossing printer to print out the stuff. And then had them feel that actual print with their fingers.
So anyway, it is something you could try. And it is free.
Another thing you could try if the child can understand English - is our app:
$1This is the app we were saying were interacting with the eyes-free google group about.
This is probably the best audio recorder app available on android for blind users.
Our next app (currently in Alpha Test) is already being tested by blind users (it has background recording, MP3 recording etc.) - and they say they are making it their main audio recorder app.
However, for your purpose you can use the current app whose link is above - it doesn't have background recording.
But what you could do is use it to have the child record sounds and play them back - it has a convenient and centrally located buttons.
NOTE: for blind users, you would use TalkBack, the screen reader for the blind which is included with Android devices - Settings - Accessibility - TalkBack - turn it ON. Not sure if an autistic child will find the sounds that makes disconcerting or not, since TalkBack makes a lot of noises like that.
But one feature these apps have is Ear Detect. In this, you can record just by moving phone to ear, and moving it away to pause. Then you can play it back. You can also flip phone so it is face down to record, and face up to pause etc.
Perhaps a better one may have been one where it played back immediately after you moved the phone away from ear.
For that you could try some of the Talking Tom Cat type of apps, which will speak back what is said (but in a usually higher pitched voice so it sounds like a cat I guess).
Anyway, just some ideas.