Here's a more complete copy of "Drimindown" than that in DT.

Drumion Dubh: Or, The Irishman's Lamentation for the Loss of his Black Cow.

Oh! there was a poor man,
And he had but one cow
And how he had lost her
He couldn't tell how,
But so white was her face
And so sleek was her tail,
That I thought my poor Drumion Dubh
Never would fail.
[Chorus]
Agus oro Drumion Dubh
Oro ah!
Oro Drumion Dubh
Mhiel agrah!
Agus oro Drumion Dubh
O, ochone!
Drumion Dubh dheelis
Go dea tu slan.

Returning from mass
On a morning in May,
I met my poor Drumion dubh,
Drowning by the way
I roared and I bawled,
And my neighbours did call,
To save my poor Drumion Dubh,
She being my all.
Agus oro, &c.

Ah, neighbours, was this not
A sorrowful day?
When I gazed on the water;
[Where] my Drumion Dubh lay?
With a drone and a drizzen,
She bid me adieu,
And the answer I made, was
A loud phillilu.
Agus oro, &c.

Poor Drumion Dubh sunk,
And I saw her more
Till I came to an island
Was close by the shore;
And down on that island
I saw her again,
Like a bunch of ripe blackberries
Rolled in the rain.
Agus oro, &c.

Arrah, plague on you Drumion Dubh,
What made you die?
Or why did you leave me?
For what and for why?
I would rather lose Padeen
Ma mhogiel beg ban
Than part with you Drumion Dubh,
Now that you're gone.
Agus oro, &c.

When Drumion dubh lived,
And before she was dead,
She gave me fresh butter
To [eat] to my bread;
And likewise new milk,
That I soaked in my scon,
But now its black water,
Since Drumion Dubh's gone!
Agus oro, &c.

Text from 'The Universal Songster', 1828. There is a 4 verse text in 'The Irish Minstrel', c 1828 (not in the 1825 ed.) Robert Owenson (Mac Eoghain) sang it at a Dublin concert in 1778, as "DHRIMMINDUH". No 18th century copy of the song seems to have survived, however. One verse and chorus was noted from a Kerry piper around 1815. Owenson's daughter Sidney (later Lady Morgan) wrote a new song for the tune for her 'Twelve Hiberian Melodies', 1805? A version of the song above, with the same original tune, was published as a sheet music song in Baltimore in the 1830's. (Copy in Library of Congress) There is a version of the song in the R. W. Gordon MSS, #1035, at the Library of Congress Folklore Archive.

There are many copies of the tune, to a late as a copy of 1912 from Chicago (but new cow song). Below are two early versions of the tune in ABC. A version is already in DT for Hughie Graham, from 'The Scots Musical Museum', #303. All tunes collected in the 20th century seem to be different from this one. Leadbelly's tune got turned into "Kisses sweeter than wine"

X:1
T:Driman Duff
N:Thumoth's '12 Scotch and 12 Irish Airs', c 1743-5
Q:56
M:3/4
K:A dorian
A/2B/2|{d}~c2B|AGA/2B/2|{d}~c2B|{c}A2G/2A/2|B2A|\
GE3/4D/4E3/4G/4|gd/2B/2c/2A/2|!G2A/2B/2|{d}c2B|\
AGA/2B/2|{d}c2B|A2B|(c/2B/2c/2d/2e/2)g/2|\
a2g|~e/2d/2Bd/2B/2|A3:|]

X:2
T:Drimen Duff
N:Oswald's Caledonian Pocket Companion, bk. 8, c 1756.
Q:56
M:3/4
K:Am
(A/2B/2)|{B}c2B|AE(A3/4B/4)|c2B|A2(G/2A/2)|B2A|\
G(D/2E/2)(G/2A/2)|{A}B3/2 (c/2 B/2A/2)|G2(A3/4B/4)|\
c2B|AE(A3/4B/4)|c2B|A2E|cc/2d/2e/2g/2|{g}a2g|\
(e/2d/2e/2)g/2a/2B/2|A2:|]