The earlier broadside version is more frank. The following is a transcription of Douce Ballads 1(97b) (see link above); the print is indistinct in a few places, and in those cases I've used the readings from Bruce Olson's transcription of an issue printed for W. Thackeray and T. Passinger (1686-1688), which can be seen at his website: The Huntsmans Delight, Or, The Foresters Pleasure. That doesn't include the two-verse preamble shown below (which I have italicised to avoid confusion), where I can't be sure of the first word or two.

THE HUNTSMAN'S DELIGHT Or, THE FORRESTER'S PLEASANT PASTIME

To the Tune of, Amongst the Leaves so Green a &c.

F r wh , 'twas thought that some ther woes withawn.
The Deer are wounded, but they are not slain,
Yet so they're wounded, that they are or'etain;
And in their taking, pitty it is shown:

The Keepers swore great Oaths, upon their lives,
They'd be as kind to them as Men are to their Wives.
The pleasant Sport this Ditty doth declare,
Of the kind Huntsmen, and the Fallow-deer.

Come all you young Maidens and lend an ear,
Come listen a while, and you shall hear
How the Keepers did sport with the fallow-deer,
Amongst the leaves so green a:
Hey down, derry derry down,
Hey down down, ho down down,
Hey down, ho down, derry derry down,
Amongst the leaves so green a.

The Keepers they wouldan a hunting go,
And under their coats each carried his bow,
All for to shoot the bonny bonny Doe,
Amongst the leaves so green a:
Hey down, derry derry down,
Hey down down, ho down down,
Hey down, ho down, derry derry down,
Amongst the leaves so green a.

They spyed five Does upon a hill,
And to shoot at them was their good will,
But none of them they ment for to kill,
Amongst the leaves so green a.
Hey down, &c.

At the first Doe they shot, and they mist,
The second Doe they clipt, and they kist;
And they laid them down where no Man wist,
Amongst the leaves so green a.
Hey down, &c.

The one cryed out unto the other,
I'm serv'd as my Father serv'd my Mother;
But yet these joys we cannot smother,
Amongst the leaves so green a:
Hey down, &c.

The third Doe she made great moan,
Because that she was big with Fawn,
Which made her to go weeping home,
From mmongst the leaves so green a:
Hey down, &c.

The fourth Doe could no longer stay,
But she must be gone her way,
For fear that the Keepers should her lay
Amongst the leaves so green a:
Hey down, &c.

The fifth Doe leapt over the stile,
But the Keeper he got her by the heel,
And there he did both kiss and feel,
Amongst the leaves so green a.
Hey down, &c.

They drew forth their arrows once again,
And they shot at another across the plain;
She sigh'd, but it was with a pleasing pain,
Amongst the leaves so green a.
Hey down, &c.

He pricked her straightways with his dart
But she cryed out she felt no smart,
And herein lay the Keeper's art,
Amongst the leaves so green a.
Hey down, &c.

These fair Does, they leapt, and they skipt
Till leaving along, at length they were tript
No sooner they fell, but the Keepers them clipt
Amongst the leaves so green a:
Hey down, &c.

The Keepers did tumble them o're and o're,
Though often they shot, they requir'd more
They never had met with such sport before,
Amongst the leaves so green a:
Hey down, &c.

These bold Huntsmen were all agreed,
And by consent these fair Does did bleed;
But after that they came often to feed
Amongst the leaves so green a.
Hey down, &c.

Great Crowds came running over the Plain,
Expecting to see these fair Does slain;
But like Fools as they came, they return'd again
From amongst the leaves so green a:
Hey down, &c.

If it be true as old Wives say,
Take a Doe in the Month of May,
And a Forrester's courage she soon will ally,
Amongst the leaves so green a.
Hey down, &c.

These Huntsmen were so gently inclin'd,
They let them rise their courage to find;
But away they tript so swift as the wind,
From amongst the leaves so green a:
Hey down derry derry down;
Hey down down, ho down down,
Hey down, ho down, derry derry down,
Amongst the leaves so green a.

There doesn't seem to be an extant example of the tune prior to 1788; Bruce Olson quotes the following:

X:104
T:LVSGREN2- Amongst the Leaves So Green, O
S:O'Keeffe/ Arnold's tune, from Calliope, 1788
Q:1/4=100
L:1/8
M:C
K:F
A B|c c c c c2 c c|d c B cd2d d|c B A B c2c c|B A G AB2B B|\
A A A A A2A A|B G G AB2A G|F2c2 {e/}d2c B|A2G2F4|:\
"Chorus"A B c2A B c2|A Bc2A Bc2|f2c2f2c2|B G G A {c/}B2A G|\
F2c2{e/}d2c B|A2G2F4:|]

The tune noted by Sharp, though rather changed, is clearly related. The midi with the DT file was presumably made by ear from the Weavers' arrangement, but is still very close to their source, the tune noted by Sharp from Robert Kinchin.