Hi Lisa
There are no suitable Carney/Carnys in the 1925 Directory, and no Trevenas at all. In the 1903 Directory - again no suitable Carneys, but Mrs Elizabeth Trevena is living at 1 The Avenue, Egerton Street, New Brighton. She was living at 28 Tollemache Street, New Brighton in 1911. You could check who else was living at that address, both via the census and the electoral rolls for the males.
From his age he should have been involved in the Great War. There were 50 William Carneys (no Carnys) receiving medals for WW1. You had to serve overseas to receive a medal, so there would have been others who were kept at home. But you may find something in the WW1 records on Ancestry. Also Findmypast will be putting online the army records for pre WW1 soldiers, both regulars and militiamen during 2011.
I am sure you have considered that his father may have been invented, and also that he may have taken a few years off his age when he got married. As he did not live long enough to draw his old age pension he could have got through life not needing to prove his age.
Has this been posted before? On FreeBMD, William Carney, Congleton, Sep (qtr) 1865. In the 1871 census he is living with parent’s Thomas and Bridget so I think you can discount the 1911 William Corny.
Both New Brighton streets are still there. If you find them on Multimap (and switch to Birds Eye view) half the houses are still there. A number are three storey so idea for lodgings, and less that 2 minutes from the ferry.
Ken