Re: "...St Marys Convent cesspit ..."
Various theories and legends exist about the Stone's history prior to its placement in Scone:
One story concerns Fergus, son of Erc, the first King of the Scots in Scotland, whose transportation of the Stone from Ireland to Argyll, where he was crowned in it, was recorded.
Some versions identify the stone brought by Fergus with the Lia Fáil used at Tara for the High King of Ireland. Other traditions contend the Lia Fáil remains at Tara. (Inis Fáil, The Island of Destiny, is one of the traditional names of Ireland.)
Despite the claim on Wikipedia
The Lia Fáil (Irish pronunciation: [ˌlʲiːə ˈfɔːlʲ], meaning Stone of Destiny), not to be confused with the Stone of Scone, is a stone at the Inauguration Mound (Irish: an Forrad) on the Hill of Tara in County Meath, Ireland, which served as the coronation stone for the High Kings of Ireland. It is also known as the Coronation Stone of Tara. In legend, all of the kings of Ireland were crowned on the stone up to Muirchertach mac Ercae c. AD 500.
The oldest Irish written sources actually claim it was lent to the Scots and not returned. Obviously the one at Tara is for the Tourists and how could you sit on it anyway?. Irish legend claims also it was Jacob's Pillow AND brought by the Tuath Dé from their city when they invaded Ireland (it can't actually be both, the Jacob's Pillow is a typical later Christian insertion).