Based on Duncan's son Alexander Earle Murray's baptism record, I think Duncan may be the same person as William, son of Alexander Murray and Isabel Gibbons of Stanhope and Barnston, Quebec.
Points in favour of this theory (see profiles for sources):
1. Alexander Earle Murray's parents lived in Barnston in 1876. One of the sponsors at his baptism was "A. Murray." The two A. Murrays in Barnston in the 1871 census were Alexander Murray, stonecutter and his son, Alexander.
2. In the 1871 census, Alexander Murray's son William was a stonecutter. In the 1881 census Duncan (going by the name William D.) was a stonecutter.
3. Alexander and Isabel's daughter Ina's 1924 obituary says she has 4 brothers and 5 sisters surviving her. Based on the 1871 census, those brothers would have been George, William, Alexander, and Fenwick. Duncan William died in 1926. Fenwick's 1933 obituary only mentions one brother, Alexander.
But, I haven't been able to find a firm record, either a marriage record for Duncan and Mary that lists their parents, or something with the name Duncan William/William Duncan Murray and his parents (or even a mention in the context of his siblings). Anyone want to help look for something?