A tablet doesn’t really make much difference in Aseprite. In Aseprite, a tablet can only move the cursor around, same as a mouse (at least currently). So, if you just hook up a USB mouse (which should be very cheap at your local office store or computer store) to the laptop, your son will be able to do everything the pros can. For blocking in large shapes (e.g. for big illustrative pieces), a tablet can be a little faster, but for most sprite work, a tablet isn’t helpful. For some aspects of sprite work, using a mouse is faster and more precise, so even artists who normally use a tablet often switch to using a mouse for most of their sprite work.
Unless your son’s laptop outright lags when Aseprite is running, you shouldn’t need a desktop. Hook up a USB mouse to it so that he doesn’t have to use a trackpad, and you’re golden!