We are not allowed to post in the RootsChat forum anything about anyone who is, or may be, still living, so I need to be a bit careful trying to answer this.
I see that William Matthew Cloonan's wife was Elizabeth McLaren, and that as someone said upthread they were married in 1899 and she died in 1937, aged 62. So she would have been born in 1874/1875. What were the names of her parents?
I cannot find the marriage of a Mr Marr to a Miss Cloonan, however. To find that you would need to see your friend's own birth certificate, which will tell you the date and place of her parents' marriage. As it's less than 100 years ago, you cannot view that certificate online.
the 1911 census lists William Cloonan, 40, and Elizabeth Cloonan, 35, in Canongate, but it lists no children with them. In 1901 there are William Cloonan, 30; Elizabeth Cloonan, 25; Mary A Cloonan, 24; and William Cloonan, 2. This is presumably the William Matthew Cloonan who was born in Newington in 1899 and died in Canongate in 1901 aged 3. There are no other Cloonan births in Edinburgh, so I am at a loss to know who your friend's mother was.