The Clochoderick stone is a particularly fine example of a glacial erratic. Composed of volcanic rock differing from that below the soil on which it rests, but similar to bedrock occurring in the hills a few miles to the north and west, and deposited here during the last ice age around 18,000 years ago.
Legend asserts its use by the druids as a site for dispensation of justice on this rocking stone. Depending on how the stone moved, with the accused in place, innocent or guilty was decreed.
It is also asserted that the stone marks the burial place of Rydderick Hael, monarch of the kingdom of Strathclyde. Considerable research establishes his crushing victory over paganism at Arthuret, near Carlisle, resulting in the conversion of the country to Christianity.
This stone is otherwise known as Clach a' Druidh. It's a massive lumpy glacial erratic boulder, over six metres long and broad, which rises four metres out of the ground. Obviously it's the rock of the druids. Slightly less convincing is to link the name with Roderick Hael, a king of Strathclyde. This page from the Geological Conservation Review says it is composed of a basalt, criss-crossed by haematite veins. A quick websearch suggests it's currently (and probably always has been) the haunt of rock climbers. If you can't get to the top, BRAC has some photos of some cupmarks that are up there.
Canmap describes two stones here. They're only about four feet high and are both 'natural stones with no artificial markings'. This folklore admittedly doesn't involve them, but is about their environment above the steep slopes down into the city.
The Glasgow chronicle (January, 1826) records the following occurrence at Paisley, on the occasion of some silkworkers being out of employment.*
"Visions have been seen of carts, caravans, and coaches going up Gleniffer braes without horses, or with horses without heads. Not many nights ago, mourning coaches, too, were seen going up the Cart above the town, with all the solemnity of a funeral. Some hoary-headed citizens relate, that about thirty years backward in their history, a famine was prognosticated in much the same way, by unusual appearances in the Causey-side. The most formidable witnesses in favour of the visions come from Neilston, who declare that they have seen the coaches, &c. two by two, coming over the braes, and are quite willing to depose to said facts whenever asked, before the Paisley magistrates."
They're probably visible at the moment, as I assume this bit [*] refers to Woeful Economic Climate.