The A part of this tune is very standard and has no sections which really sound like they need chord IV. Chord V goes in the fourth and eighth bars exactly as you would expect, returning to chord I to mark the end of the A section in bar eight. However, the B part is very unusual in that it clearly has to begin on chord V, and stay there for a whole four bars! The notes in the first bar of the B part for example are E AAA- all notes taken from an A major chord (A, C# and E).
As I got bored of playing D for two whole bars, I have replaced the second D bar with the same chord in its first inversion. This is basically like playing the same chord but adding a bassline for a sense of movement.
Bars three and four were previously both bars of A. If you have a long period on one chord you can always work your way round the circle of fifths in order to LAND on that chord. In this instance I have resolved down a fifth to A from an E chord (E-D-C-B-A). As we are in the key of D ionian, the E chord has to be E minor (use your Amazing Mode Wheel to check the chords available if you can’t remember them), leaving my previous chord block of A / A / to now become Em / A / . The A chord then resolves to D, continuing on around the circle of fifths. Chord progressions which move round the circle of fifths in this way are very satisfying to the listener and a II – V – I progression like this one (Em – A – D) is a common way to finish sections in all kinds of music.
Firstly, in this version I have replaced all the chords with “the right kind of seven chord”. For tunes in a major key this means that chords I and IV can become major 7 chords, chords II, III and VI become minor 7 chords and chord V becomes a dominant 7 chord. Both Bm7 and F#m7 are valid substitutes for a D major chord- B minor is its related minor chord and F#m is the minor chord two notes above the major chord, which consequently contains two notes in common (D major is D, F# and A and F#m is F#, A and C#).
In the B part I have replaced a long section of A with a nice slidey chord run which is outlined below. I have finished it off with an E9 chord. This works because any dominant or altered dominant chord can theoretically replace chord V, aka 7, 8, 11, 13, #9, ♭9, 7♭5 or 7#5 (bear in mind that some of these options might sound TOO jazzy in some folky contexts).