AS a model, you might try harmonies in thirds and sixths. Then try some in fifths. Even if a use of these intervals doesn't always fit the chords, they can be modified to do so.

Another way is to have the group just sing the chords of a song by each member taking the root, third or fifth and sometimes the 7th of the chords. Have them sing a wall of harmony duplicating the chords by taking their own "voices". Use a two-chord song to start with. This helps tune the ear to the chord harmonies and helps the person derive their harmony part from this source.

Another way is for each student to write down or remember a specific harmony part and test it against the melody. Does it work? How does it need to be modified?

The best harmony part in my view are ones that are not contrived but flow naturally from the harmonizer. The best arrangements of folk or bluegrass or whatever come from those who know how to harmonize and don't follow someone else's arrangments. The group makes it's own arrangment.

Frank Hamilton