Mrs. Murphy: I've checked The Lester S. Levy Collection of Sheet Music and The Library of Congress American Memory Collection – usually the best sources for sheet music – but I've found only lyrics, not notes.

However, since I did find one version apparently not posted here before, I might as well post it for posterity:

Copied from http://memory.loc.gov/cgi-bin/query/r?ammem/amss:@field(DOCID+@lit(as201910)) :

JOHNNY IS GONE FOR A SOLDIER

I'll trace these gardens o'er and o'er,
Meditate on each sweet flower,
Thinking of each happy hour.
Oh, Johnny is gone for a soldier.

CHORUS: Shool, Shool, Shool, agrah!
Time can only ease my woe,
Since the lad of my heart from me did go.
Oh, Johnny is gone for a soldier.

Some say my love is gone to France,
There his fortune to advance,
And if I find him, it's but a chance.
Oh, Johnny is gone for a soldier.

I'll sell my frock. I'll sell my wheel.
I'll by my love a sword of steel,
So in the battle he may reel.
Oh, Johnny is gone for a soldier.

I wish I was on yonder hill.
It's there I'd sit and cry my fill,
So every tear may turn a mill.
Oh, Johnny is gone for a soldier.

I'll dye my dress. I'll dye it red.
All over the world I'll beg my bread,
So my parents may think me dead.
Oh, Johnny is gone for a soldier.