Here's the words of Paddy Berry's version as given in his book "Wexford Ballads" - I haven't checked it against the Youtube version.:

Murphy's Running Dog

My usual occupation is to turn and temper clay
Last year I turned to betting and I found it would not pay
I ran my dog in Wexford Park and I ran him in Ballystraw
In the latter place he lost the race when he stopped to lick his paw

Chorus
Bad look to gambling I'm in an awful fix
Out of four pound six and eight pence all I have is one and six
We'll go down to Shea's or Kenny's and we'll drink a glass of grog
And go home around Dunbrody singing Murphy's Running Dog

I ran him in Kilkenny and I ran him in Tralee
He ran in Enniscorthy and he ran in Carberry
He won a race in Thurles and he lost one in Athlone
He ran away with the race that day – but he stopped to lick a bone

You'd here him yell a mile away when he is in the slips
And when the hare he sees, he shakes his knees and smacks his lips
I think Compile's about a mile and if he does not lose
Tis off we'll start to Matty Hart's and then go on the booze

We'll order two half barrels to be tapped upon the bridge
And upon the wall we'll drink it all, from there we will no budge
We'll sing the praise of today's craze with Cherries' beer and grog
And drown all care I do declare with Murphy's Running Dog

And Barnes's "Biddy the Nailer" 'twas many's the race she ran
In the wet North Slob, so help me Bob, was the first my "Juggler" won
When Mr. Barr yoked up his car, home through Wexford we did jog,
And every hare I do declare was picked up by my dog

I hope you're not offended by those verses written here
I long to see the committee and stewards do well next year
Bring your true love to Kilmarnock boys and if my greyhound wins
We'll dance all night till broad daylight in Costello's of Saltmills

Regards