No listing for this song in either the Digital Tradition or the Traditional Ballad Index. At this time, Roud has only one entry:

An Account of the Gibbeting of William Jobling At Yarrow Slake
First Line After the body of Jobling had hung on the drop... [Prose]
Roud No V29433 [Search for V29433 in the current indexes]
Source Vicinus, Ballads of the Industrial North pp.40-41
Printed : Street literature : Broadside facsimile

I bought the Martha Vicinus book, and it arrived today. I was disappointed to find that it's a newspaper clipping, not a song. Here's the text:

An Account of the Gibbeting of William Jobling At Yarrow Slake
On Monday August 6th, 1832, pursuant to his sentence, for the murder of Nicholas Farles, Esq., resident Magistrate of South Shields with a correct Representation of the Gibbet.

After the body of Jobling had hung on the drop at Durham for an hour, it was taken down, the clothes were stripped off, but no incision made, it was covered over with pitch, and the cloths in which he was hanged were then replaced.
On Monday morning, at 7 o'clock, the body was brought in a four-wheeled wagon, drawn by two horses, from Durham, escorted by a troop of the 8th hussars, and two companies of the 18th regiment of Infantry, Mr. Griffiths; the under-sheriff Mr. Frushard, the gaoler, officers of the gaol, &c. &c.
They proceeded by way of Chester-le-street, Pictree, Sludge Row, Portobello, over the Black Fell, to White Mare Pool, and thence, by the South Shields turnpike road, to Jarrow Slake, where they arrived at half-past one o'clock. The spectators were not numerous perhaps 1000 in number, and not many pitment amongst them; arising, probably, from a meeting ??? held by them that day on Bowden Fell.
[portion missing - corner torn off]
......thighs, the bowels, the breast, and the shoulders; the hands were hung by the side and covered with pitch; the face was pitched and covered with a piece of white cloth. Being laid on a hand barrow, the body was fixed nearly opposite the spot where the murder was committed, and about 60 yards from high water mark.
The gibbet is formed of a square piece of oak, 21 feet long, and about three feet in diameter, with strong bars of iron up each side. It is fixed in a stone 1-1/2 (?) ton weight, which is sunk in the Slake. At high water there will be 16 or 17 feet of the gibbet visible.
The body was then hoisted up and secured, and left as a warning for the futer (sic), and a memento of the past.
There will be a Military guard on the spot for a fortnight.
The procession passed on its route without the least interruption; and on the spot, every thing was quiet and orderly. One solitary voice only, as thye carried the body from the waggon to the gibbet, shouted out "Take the police with him, over the water."

The following Handbill was distributed in Shields and the neighborhood:
NOTICE TO THE PUBLIC. - In the act of Parliament ordering the dead Bodies of Murderers to be hung in Chains, there is a Clause inflicting the punishment of Transportation for seven Years, upon all who may be guilty of stealing the Body from the Gibbet.

---

And here's a chilling description of Jobling's punishment: http://blog.twmuseums.org.uk/a-grim-death-for-a-most-heinous-crime%E2%80%A6/