I did a Google search and turned up a discussion of his episode of "Deadwood" and a question about the song. The tune is what later became known as the "Cowboy's Lament" but there was a 19th barroom version, apparently... see below for explanation.
> A few episodes ago Al tells Johnnie and Dan about the
> Amateur Nights the acting troupe had in the old days.
> I think Al probably used to be a part of them (his
> s singing voice was very good.)
> The song Al was singing was originally an Irish tune
> called the Bard of Armagh latter in America changed
> to Cowboys Lament but the lyrics/version Al was
> singing was an 19th English barroom version called
> The Unfortunate Rake(or Pills of White Mercury)
> (From Digital Tradition but got a question about an
> old song go to \www.mudcat.org)
> "THE UNFORTUNATE RAKE
>
> As I was a-walking down by St. James' Hospital,
> I was a-walking down by there one day,
> What should I spy but one of my comrades
> All wrapped up in flannel though warm was the day.
>
> I asked him what ailed him, I asked him what failed
> him,
> I asked him the cause of all his complaint.
> "It's all on account of some handsome young woman,
> 'Tis she that has caused me to weep and lament.
>
> "And had she but told me before she disordered me,
> Had she but told me of it in time,
> I might have got pills and salts of white mercury,
> But now I'm cut down in the height of my prime.
>
> "Get six young soldiers to carry my coffin,
> Six young girls to sing me a song,
> And each of them carry a bunch of green laurel
> So they don't smell me as they bear me along.
>
> "Don't muffle your drums and play your fifes
> merrily,
> Play a quick march as you carry me along,
> And fire your bright muskets all over my coffin,
> Saying: There goes an unfortunate lad to his home."
The original song was a traditional Irish folk ballad called
The Bard of Armagh
Oh list' to the tale of a poor Irish harper
And scorn not the string of his old withered hands
But remember those fingers they once could move sharper
To raise up the strains of his dear native land.
It was long before the shamrock, dear isle's lovely emblem
Was crushed in its beauty by the Saxon's lion paw
And all the pretty colleens around me would gather
Call me their bold Phelim Brady, the Bard of Armagh.
How I love to muse on the days of my boyhood
Though four score and three years have fled by them
It's king's sweet reflection that every young joy
For the merry-hearted boys make the best of old men.
At a fair or a wake I would twist my shillelah
And trip through a dance with my brogues tied with straw
There all the pretty maidens around me would gather
Call me their bold Phelim Brady, the Bard of Armagh.
In truth I have wandered this wide world over
Yet Ireland's my home and a dwelling for me
And, oh, let the turf that my old bones shall cover
Be cut from the land that is trod by the free.
And when Sergeant Death in his cold arms doth embrace
And lull me to sleep with old Erin go bragh
By the side of my Kathleen, my dear pride, oh place me
Then forget Phelim Brady, the Bard of Armagh.
So there are many versions of what became known as the "Cowboy's Lament" or "Streets of Laredo" in America, but apparently they all stem from the original Irish tune Bard of Armagh.