One can harmonise a surprising amount of melodies by saying that each chord must be either
a) the same chord as the previous melody note
b) one chord clockwise on the cycle of fifths
c) one chord anticlockwise on the cycle of fifths
If you allow for certain chords to have their relative minor/major then apart from occasional exceptions, you have the basis of the whole of classical harmony.
Sorry, it really is that simple.
Edinburgh Recording Studio Windmill Sound