Here ya go, transcribed from the sheet music at The Library of Congress American Memory Collection:

JOHN RILEY'S ALWAYS DRY
Words, Edward Harrigan. Music, Dave Braham. 1881.
As sung in Edward Harrigan's comic play, "Mulligan's Silver Wedding."

I have an old companion, John Riley from Tralee.
In fair or cloudy weather, John Riley's seen with me.
His heart is like a mountain, His honor ye can't buy,
But elbow bending is his fault. John Riley's always dry.

CHORUS: Bass's ale by the pail
He would order Rosanna to go out and buy.
"Dublin stout!" he would shout,
Keep drinking and never say die.
Whiskey prime, gin and wine,
He would hand down a bottle and merrily cry,
"My Rose Ann, fill the can,
For honest John Riley's dry."

It's ev'ry morning early, John Riley's out of bed.
Sure never a feather bolster lies under Riley's head.
It's when the sun is rising so eager and so sly,
He slips out for his bitters, boys. John Riley's always dry. CHORUS

His father often told him when John was but a youth
That ev'ry mortal Riley all died from whiskey drouth.
Of course it is a failing, the poor man can't deny.
'Tis but a freak of nature, boys: John Riley's always dry. CHORUS

What puzzles all the doctors John Riley ever met
Is, fresh or salty water can't make John Riley wet.
Sure he must have the liquor, rum, brandy, gin or rye,
And should he miss the bottle, boys, John Riley'd surely die. CHORUS

[JOHN RILEY'S ALWAYS DRY is included on the various-artists album "Don't Give the Name a Bad Place: Types and Stereotypes in American Musical Theater, 1870-1900" New World CD 80265, 1996.]