Bass in a car is easy. I'd just search Craigslist for subwoofers or sub boxes. Fosgate, MTX, JL Audio, Infinity, Alpine, Memphis, Eclipse, MB Quart, there's bound to be something worthwhile nearby at an excellent bargain, and probably already bundled with an amp. People get married, have kids, get minivans, and get rid of their subwoofers. I do recommend vented, as I've heard vented 8's that felt and sounded like 15's. Also, since your son's car is so small, I think an 8 would be plenty big enough, and he can still throw stuff in the trunk when he needs to.
Also, plan to get a 1 fard cap. Not only will it make the sub amp more capable of handling peaks, but it'll also save some wear on the car battery. I noticed before I got a cap I was replacing my car battery every couple of years; but after, my battery would last at least 5.
If you want to treat your son, get him a miniDSP and a 4-channel amp (again, probably available on Craigslist) for the cabin speakers, and flatten his midrange with a laptop and a measurement mic. If he's got a factory head unit, Crutchfield or fleabay or somebody probably offers an adapter for head unit out to RCA pre-amp. Upgrading his front speakers would also be a good idea. Maybe Craigslist again?
