There must be a link, particularly given the fact the surname is so uncommon, especially in Cavan. I've come across it most often in county Down.
The only Diniver/Denvir I could find in any records for Cavan was Daniel so that's why assumed he would be the connection to my great grandmother. He could still be, albeit not her father. Possibly an uncle, brother or cousin of her father?
Let me tell you what I know. In 1857 Daniel Diniver is listed as living in Ballynahaia, Drumgoon Parish (Griffiths Valuation, June 1857). In a Landed Estate record dated Nov-Dec 1859, a Daniel Denvir is listed, same location. In both he has 8 Acres, 1 Rod & 36 Perches.
Now for some family folklore. My maternal grandfather always said that his own maternal grandfather was French. The story was that his name was Denoir and he worked for the Coote family. After his daughter Mary was born, to a woman believed to be Mary McDonald, he died. Mary McDonald re-married a man called Brady, and the child took her step-father's name. So far so good...(take all of that with more than a pinch of salt; just hearsay, nothing proven!)
On the 4th of February, 1869, James Smith, a bachelor of full age, a labourer from Newry, and son of Hugh Smith, married in the Newry roman catholic church, by a Rev T McGivern, one Mary Brady, a spinster of full age, a labourer from Tullivin (sic), Cavan, and daughter of Patrick Brady. Witnesses present were Mary Brady & Michael McConnell (just to emphasise that's been transcribed as McC).
Now here's where it gets interesting. In the same land records from which I've quoted above there are Smiths and Brady (both common in Cavan) but also - in 1857, one Mary McDonnell (McD); and in 1859, one Mary McDonald (widow).
Confusing isn't it? You ain't heard nothing yet!

Mary Smith, born Sept 14, 1871 to James Smith (flax scutcher), Lisagoon and Mary Smith (civil & church) formerly Denvir (civil) in Drumgoon parish (same parish as Daniel Diniver/Denvir).
Catherine Smith, born Aug 15, 1873 to James Smith (labourer), Drumnagran and Mary Brady (church)/Smith formerly Denvir (civil) in Kilsherdany parish.
Patrick Smith, born 1876 to James Smith (labourer), Drumnagran and Mary Denivor (church)/ Smith formerly Denipher (civil) in Kilsherdany parish.
Bridget Smith, born February, 1878 to James Smith (occupation unknown) and Mary Devine (church) in Kilsherdany parish.
Eugene Smith, born July 5, 1880 to James Smith (labourer) and Mary Denivor (church)/Smith formerly Brady (civil) in Kilsherdany parish.
James Joseph Smith (my grandfather) born July 3, 1882 to James Smith (scutcher) and Mary Brady (church)/ Smith formerly Dennifer (civil) in Kilsherdany parish.
Margaret Elizabeth born Nov 21, 1884 to James Smith (scutcher) and Mary Smith formerly Brady in Kilsherdany parish.
The six listed above, apart from my grand-father, are definitely his siblings therefore Devine for eg is quite obviously wrong. But the rest are variations on a theme: Denvir/Diniver.
All records and obtained transcripts have been checked and verified by me, except the marriage record from 1869 (can't verify if Michael is McConnell or McDonnell).
Confusing eh?
