'Stob' perhaps refers to the stones' stumpy appearance (those with a more violent imagination could create a story around the alternative meaning of 'stab').
Tradition has it that the Kings of the local Yetholm gypsies were always crowned here. This page of 'The Scottish Journal of Topography, Antiquities, Traditions, &c.' describes the death of the former king, Will Faa, in 1847, and his successor's riotous coronation. http://books.google.co.uk/books?id=jQsIAAAAQAAJ&pg=RA1-PA64
A good amount of whisky was being drunk, and at one point the attendants accompanying the king on his white horse up to the stones thought it'd be funny to 'tickle the horse behind' and poor Charles the First 'embraced his mother earth', not ideal for a man over 70. But after a glass of whisky he was ok. Also on the way,
A hare was started, which being pursued by the Royal retinue, was quickly ran down. On arriving at the Stob Stone, the procession halted for a few minutes, when his Majesty dismounted from his palfrey, and mounted the huge block of stone, when he was decorated with the said hare, which was tied across his shoulders (his Majesty being a keen sportsman), as a trophy of game killed upon his own land, and which he continued to carry during the remainder of the procession.
Here, also, while seated upon the stone, his Majesty's head was anointed with whisky, instead of oil, and his health drunk in deep potations of the same, amidst immense cheering. The procession then returned to the village, where his Majesty was loudly cheered.
I don't know what the Megalithic Cognoscenti of the Borders will think of these two stones, but I'm intrigued to find out. They are both quite sturdy, one standing, the other lying, at over five feet. The RCAHMS puts them down as medieval boundary markers - but this was from an official visit back in 1938, so perhaps there's hope that these stones could be brought into the tma fold?