Hi Gillian,
You've already had a bit better success than me already.
I did see the death of James Bernard; I assume it's the correct one and the unnamed son of Bernard and Rosina? If so, what details are provided on this certificate; such as birthplace and parents' details (more importantly, who registered it?).
The same questions for Patrick, b. 1867. It would be interesting to try and locate a death for him too.
The McKenneys/McKennas appear on the 1851 census at Reids Close, Canongate. As I thought, the family are of Irish origin; Michael was born c. 1809 in Ireland and is described as a hawker. Bernard though appears to be born in Edinburgh. This definitely helps to try and track him again.
I found on the 1901 census ...
Address: West House, Royal Edinburgh Asylum, Craig House Road, EdinburghBernard Mckenna, m, patient, 58 [b.c. 1843], formerly sailor, b. Edinburgh
Sailor doesn't really match with anything we've had before (and I've considered it could be tailor given his father was some sort of clothes dealer/hawker) but it's a possibility. He could appear in previous censuses in various hospitals/asylums; unfortunately, patients were often listed under their initials and/or with various incorrect details.
hume