Donna,
Welcome to Rootschat.
Not such a long shot.
According to Scotland's People, there were only 6 (*) Rennies born over the period you state, 1 of whom was born in St Rollox in 1934.
Unfortunately, the record is too recent to view online.
Unless you can visit Glasgow or Edinburgh, you would need to purchase the death record from GROS.
The GROS ref is 644/08 2254
Dave
Cost is £12.
Info on how to obtain extract..... http://www.gro-scotland.gov.uk/famrec/bdm.html
PS The info you should get on the document would be exact time and date born, where born, details of both parents.
(*) Names removed to protect people's identity.