no thirds above are ok to start, but its predictable, sixths below area bit better but still predictable.Iremebe asking loiusa killen what was the first song you accompanied on concertina he said" jug of punch with sixths all the way through.
my advice is first work out the chords, then using the chords as a guide., try and avoid similiar motion if you can,even going in a straight line while the melody is going up is better, but try and work in some opposite motion if you can or if not play the same note, for example if the melody was in the key of gmajor and went gbd, try ggg or g, down to d, up to g, but you have tpo also mess about using your ear