This is the set of chords I use..

A(Am)las, my love, you (G)do me wrong
To (F)cast me off dis(E)courteously,
For (Am)I have lovèd (G)you so long,
De(F)lighting (E)in your (Am)company.

(C)Greensleeves was (G)all my joy,
(F)Greensleeves was (E)my delight,
(C)Greensleeves was my (G)heart of gold,
And (F)who but my (E)lady, (Am)Greensleeves.

I use a varied arpeggio pattern, occasional bass runs, bass notes planned out to harmonize with the voice. It's also possible to play the melody (intermingled with partial arpeggios) between verses when desired. I capo on either the 2nd or 3rd fret, depending, putting it in Bm or Cm.

I think I snitched this from Richard Dyer-Bennet's song folio way back when. He does it in Em. I transposed the same chords to Am and capoed up.

Don Firth