This large stone stands within the grounds of the Swallow Hotel (formerly the Graystane Hotel) just off the main Dundee-Perth dual carriageway, the A85. A small road to Denhead of Gray leads off the roundabout, and there is ample car parking at the hotel. Ask for permission to view the stone, which is readily granted. It lies behind the Conference Centre to the right of the main hotel. Adjacent to a section of railing, there are no cup marks or similar, though there is evidence of carved initials on the north facing - probably 200-300 years old.
The "Paddock Stane," a large rude block, stands in the same locality [as a stone circle], and in its vicinity stone coffins, containing rude clay urns and human bones, are frequently found. Tradition points to this stone as that which the devil threw across the Tay from one of the Fifeshire hills, when he saw St Boniface building his church at the estuary of the burn of Gowry; but, mistaking his distance, the stone fell nearly a mile farther north, and rested on the spot where it now lies!
The story seems to link in with two stones near the church itself, but they're on the beach apparently:
When the Yowes O' Gowrie come to land,
The Day o' Judgment's near at hand.
A prophecy prevalent in the Carse of Gowrie and in Angus-shire. The Ewes of Gowrie are two large blocks of stone, situated within high-water mark, on the northern shore of the Firth of Tay, at the small village of Invergowrie. The prophecy is ancient, perhaps by Thomas the Rhymer, and obtains universal credit among the country people. In consequence of the natural retreat of the waters from that shore of the firth, the stones are gradually approaching the land, and there is no doubt will ultimately be beyond flood-mark.
It is the popular belief, that they move an inch nearer to the shore every year. The expected fulfilment of the prophecy has deprived many an old woman of her sleep; and it is a common practice among the weavers and bonnet-makers of Dundee, to walk out to Invergowrie on Sunday afternoons, simply to see what progress "the yowes" are making!
From 'The Popular Rhymes of Scotland' by Robert Chambers (1826) p 97, which you can read on Google Books.
The PSAS article mentions the Goors o' Gowrie too, but doesn't mention any devilish connections - though some internet pages seem to consider them additional diabolical missiles aimed at the church. The PSAS article says "There is nothing in their appearance to attract notice, and it may now be said that they have all but 'come to land' since they are separated from the common course of the Tay by the embankments of the Dundee and Perth Railway." Oh well.
Another thing that links them is that they're made of the same stone (allegedly):
On the road to Liff, about a mile from the Tay, stands a very large boulder of gneiss, perfectly isolated, vulgarly termed the "Paddock Stane;" and two more of the same sort are to be seen at the extremity of Invergowrie Bay, within a short distance of the land.
From the New Statistical Account, v11 (1845) p575.