Two-part harmonizations often do make a sequence of chords. The usual trick for post-mediaeval music is to use parallel thirds above or sixths below the melody, rather than fifths and fourths. For this example

E D C - | E D C - | G F E - | G F E - |
G F E - | G F E - | B A G - | B A G - |

If you want to extend that to triads or more complex chords, the extra notes are usually obvious.

Will, did you really mean to keep the same harmonic sequence for bars 3 and 4 as you used in bars 1 and 2?