I'm not a natural harmony singer but got by singing in a large group. I had trouble when we introduced some West Gallery (Sacred Harp) pieces into our repertoire because you have to stick exactly to the dots and the group becomes a choir. In pieces like these the lower parts are hardly even tunes, and I found it uphill work.

I succeeded by having a CD of the first couple of verses, which I played and practised with. I know something similar has been tried with your singer, and suggested above a few times too, but the little difference with my CD was that just my part was sung solo, several times, alternating with full parts with my part on slightly higher volume. That really helped. Being rote learning it depends on frequent repetition, but shouldn't take too long. It'sjust a start really. Learning other parts later gets easier, and harmony singing starts getting normal.

Singing rounds sounds like an excellent idea too.

He can learn a melody and sing it unaccompanied in perfect pitch, so he'll be fine after a while. Just needs to practice different stuff as often as possible. Let him know when he comes up with a line that really works. Confidence is a big part of it.