As they died in the 1950's it is more likely that they would be buried in one of the major cemeteries.
Depending upon where they lived in Argyle Street and also any area where the family associated their links :-
you have Western Necropolis, The Necropolis, Sighthill, St Kentigern, Dalbeth, Eastern Necropolis and as an outside chance the Southern Necropolis.