For the kind of song for which "singing in harmony" is defined at all, the usual method (that most of us started with when still very young) is:
a) Sing a third below the melody, major or minor so that you do not leave the scale/key,
b) Whenever that sounds wrong, i.e. does not belong to the imagined chord, try a sixth below the melody, or a third above it,
c) Sometimes it is possible to use a fifth to smooth the transition between a passage in thirds and one in sixths - the technique is called "horn fifth".

To add a third voice, try to find the notes that are missing for the chord (triad), but only if it is singable without big jumps. A fourth bass voice will mainly sing the base notes of the chords.

Listen to a lot of music you like and try to find out how they do it. Deaf people will never be good composers, however hard they study with excellent books and teachers.