My suggestions, don't undersize it. A 9 year old can play on a standard size cabinet and a standard size cabinet doesn't really take up any more space than most "small" cabinets. If you build him something little then he is going to grow out of it in the blink of an eye.
Don't use a Raspberry Pi. The people who suggest you do so are well meaning but misled. It is still the worst thing you can put in a cabinet, a 10 year old PC will run rings around it. The only reason it has the popularity that it does is because the people making bootleg cabinets to sell use them because they are cheap and they can copy the software over and over again, and they don't care if the end user can't fix it when it stops working 6 months later.
Install 6 buttons per player. It will cost a whole $6 more than 4 buttons, and you might as well do it now. I have had my mame cabinet for 16 years now, your 9 year old son has no idea what he is going to want in the future. Don't use cheap joysticks. Happ Super is good for an American style stick, and what I suggest for younger players. I would suggest avoiding the Asian style sticks, the good ones look exactly like the terrible ones at first glance and the good ones cost more than a decent American style stick does.