http://www.geograph.org.uk/gridref/NS622398 - it is in the parish of Avondale.
It is, as mentioned, a Category B Listed building
http://portal.historicenvironment.scot/designation/LB1289 - the information on the 'British Listed Buildings' web site is mirrored from this source, Historic Environment Scotland, which is the agency that decides what is and is not listed.
It's not on Charles Ross' map about 1773
https://maps.nls.uk/view/74400268 but it is on William Forrest's map about 1816
https://maps.nls.uk/view/74400273.
The 1855 Valuation Roll at
www.scotlandspeople.gov.uk lists William Leiper as proprietor and occupier of 'Stobieside or Drumboy', suggesting that the name of the farm may have been changed at some point. (Could Drumboy be a mistranscription of Drumclog?)
It's unusual to find a farm owned by the farmer - most farmers were tenants. Interestingly there are also John and Robert Leiper listed as proprietors of single farms or houses, and Andrew, James, Mrs and possibly another John Leiper as tenants of other farms.
If I were looking for earlier references to a place, I would go for the Registers of Sasines, which are the records of transfers of ownership of land. See
https://www.rootschat.com/forum/index.php?topic=26232.0The index to the Lanarkshire Registers of Sasines 1720-1780 mention several Leipers in Strathaven (the older name for Avondale) but none mention Stobieside.
The National Library of Scotland has the most extensive and readily accessible range of old maps, but the British Library also has a map collection, including at least one that I know of that isn't in the NLS, so there are very likely to be more. Though I think that what you really need is to find out when Stobieside was first sold, and then look for estate plans either prepared for the sale, or for rental and estate records before the sale.
Drumclog is listed as the property of the Duke of Hamilton, so I would imagine that Stobieside was originally also part of his estates.
The Statistical Account of the parish, written in 1793, is interesting background reading.
https://stataccscot.edina.ac.uk/static/statacc/dist/viewer/osa-vol9-Parish_record_for_Avondale_in_the_county_of_Lanark_in_volume_9_of_account_1/Among other comments it says that the Duke of Hamilton is the feudal superior of the whole parish, and proprietor of about a third of it; and that there are many small proprietors ('heritors'). I wonder whether the Hamilton Estates sold off small parcels of land at some point before 1855? Perhaps Stobieside was split off from Drumclog at such a time?
According to the National Register of Archives for Scotland
https://catalogue.nrscotland.gov.uk/nrasregister/welcome.aspx most of the estate records of the Dukes of Hamilton and Brandon are privately held, though some earlier ones are in the National Records of Scotland.