I think Tex Ritter, whose son John Ritter carried on the family name as a popular actor in TV sitcoms like Three's Company and Hooperman, was the first to record the song under the title Rye Whiskey in 1932.

Perrow also has a better version under the title "The Drunkard's Song" which was also collected in 1905.

Here are Tex Ritter's lyrics from and on-line site:

RYE WHISKEY- Tex Ritter
Recorded in 1932- NYC

Jack o' Diamonds, Jack o' Diamonds and I know you of old
You've robbed my poor pockets of silver and gold.
It's a whiskey, you villain, you've been my downfall
You've kicked me, you've cuffed me, but I love you for all

CHORUS: It's a whiskey, rye whiskey, rye whiskey I cry
If I don't get rye whiskey, well, I think I will die

I'll eat when I'm hungry, I'll drink when I'm dry
If the hard times don't kill me, I'll lay down and die
I'll tune up my fiddle and I 'll rosin my bow
I'll make myself welcome, wherever I go

Rye whiskey, rye whiskey, rye whiskey I cry
If a tree don't fall on me, I'll live till I die

Beefsteak when I'm hungry red liquor when I'm dry
Greenbacks when I'm hard up and religion when I die
They say I drink whiskey, my money's my own
All them that don't like me, can leave me alone

Rye whiskey, rye whiskey, rye whiskey I cry
If a tree don't fall on me, I'll live till I die

Sometimes I drink whiskey, sometimes I drink rum
Sometimes I drink brandy, at other times none
But if I get boozey, my whiskey's my own
And them that don't like me, can leave me alone

Rye whiskey, rye whiskey, rye whiskey I cry
If a tree don't fall on me, I'll live till I die

If the ocean was whiskey and I was a duck
I'd dive to the bottom to get one sweet suck
But the ocean ain't whiskey and I ain't a duck
So we'll round up the cattle and then we'll get drunk

Rye whiskey, rye whiskey, rye whiskey I cry
If the whiskey don't kill me, I'll live till I die

My foot's in my stirrup, my bridle's in my hand
I'm leaving sweet Lillie, the fairest in the land
Her parents don't like me, they say I'm too poor
They say I'm unworthy to enter her door

It's a whiskey, rye whiskey, rye whiskey I cry
If I don't get rye whiskey, well, I think I will die

Sweet milk when I'm hungry, rye whiskey when I'm dry
If a tree don't fall on me, I'll live till I die
I'll buy my own whiskey, I'll make my own stew
If I get drunk, madam, it's nothing to you

Rye whiskey, rye whiskey, rye whiskey I cry
If a tree don't fall on me, I'll live till I die

I'll drink my own whiskey, I'll drink my own wine
Some ten thousand bottles I've killed in my time
I've no wife to quarrel, no babies to bawl
The best way of living is no wife at all

Rye whiskey, rye whiskey, rye whiskey I cry
If a tree don't fall on me, I'll live till I die

Way up on Clinch Mountain I wander alone
I'm as drunk as the devil, oh, let me alone
You may boast of your knowledge an' brag of your sense
'Twill all be forgotten a hundred years hence

Rye whiskey, rye whiskey, you're no friend to me
You killed my poor daddy, God damn you, try me