I have one of these Walkman Sports WM-AF59's, but the volume dial broke off recently. Can I glue it back on?

Depends on what the damage is I would think. Could you post a shot of the your walkman opened up with the covers taken off? That way we would know what we're dealing with and could advise further. There are some very talented people round these parts

Agree with Nak D, i pull them apart all the time so would be able to advise better if i saw the damage