Are you asking if you can get an Advance ticket just for him? I think so, as you asked before if you could travel one way with a child and the other way alone and still get the child a discounted ticket, and the answer was yes. However you will need to be quick, as Advance tickets at a reasonable price may sell out!
If you are asking if you can buy a walk-on fare for him to combine with your Advance ticket, I do not know if that is possible or not.
See previous topic posts 12-15.
Note that it says "return". AP fares are only available in singles. I do not know if that affects the situation.
If you cannot buy an individual 'CHFAM' ticket, then it may be possible to change your ticket by paying a £10 admin fee, plus the cost of your son's ticket, if that is cheaper than buying a new ticket for your son. I do not know for sure if this is possible or if it will be good value as I do not know the journey.
In any case, the only way your son will be paying 60% off the half fare of the price you paid is if you get him a ticket from the same quota that you got. With every day that passes, the chances of getting a ticket from that quota diminishes. So get yourself to a booking office sooner rather than later.