Hi Joe, I've quite a bit of information re the Cooney's (Katherine was my great-great grandmother). Below is an extract from a document my mother gave me, researched and complied by Bernadette Jury in 1987, regarding Simon and Kate's deaths.
"Simon died on 7 August 1920 at North Adelaide aged 67. He had suffered a stroke while working and was taken to hospital. He had made a will on 8 July 1920 and he bequeathed 'all my wordly possessions at the time of my decease to my wife Katherine Cooney for her personal use and benefit absolutely the same to be passed on at the time of her decease to my two sons Philip Joseph Cooney and John Dominic Cooney to be divided equally between them'. The value of the estate was 3,175 pounds. The bakery/grocery business was sold two years later and Kate and her two sons bought the Hyde Park Hotel, which was opposite the bakery. They remained there until Kate's death on 10 June 1928 aged nearly 80. Her body was on view in her bedroom and the grandchildren were told to walk around her, touching her as they passed, and they would then never forget her. Simon and Kate were buried at West Terrace. Originally a large Celtic Cross stood above the grave, but in later years this was vandalised and pulled off the plinth. It was too costly to repair and was completely removed leaving just the base, which carried the inscriptions. Kate made a will on 25 August 1920 and in it she gave 100 pounds to four of her sons. Sons John and Phillip 'equally divide remeinder of my porperty all Shares money in bank or aney mones or Property which may come due to me and all my furniture and Personal belongings'. (Spelling as per will). Her estate was valued at 84 pounds when she died. It is interesting to note that Kate signed her will as Katherine Cooney, and Simon called her Katherine in his will." I hope this fills in some gaps. Kind regards Anita.