At that time, the closest Catholic burial ground was St Peter's Dalbeth. Quite a distance from the "South Side", as Glasgow people have always called the Gorbals/Tradeston areas of the city. (Sometimes shortened to S.S. when written).
Anyway, it's not impossible that your ancestors are buried there and all the records for St Peter's are now on-line at Scotlandspeople. There is a huge burial ground in the Gorbals, with good records as far as I know but I've never had occasion to search them. If there are pauper's burials involved you will almost certainly never find the exact grave as no markers were ever erected.
If you suspect that some of your ancestors did have a pauper's burial, check the Poor Relief claims (if you haven't already done so), held at the City Archives in the Mitchell Library, North St, Glasgow. Some of the information in these claims is phenomenal and I advise you to check them. The area you are looking at would have come under Govan Combination Parish. (For Poor Relief purposes).
There are a couple of threads on this Forum concerning St Peter's and Old Dalbeth (2 Catholic burial grounds side-by-side) and Gerry Farrell, one of the contributors, is the acknowledged expert on that area, he will point you in the right direction, that's for sure.
Good luck with your research and if in doubt, ask this Forum for advice, we are a bunch of know-it-all's here