I can’t find anywhere of that name in the usual sources. It is likely to be a corruption but I can’t suggest what that might be in Ireland.
I searched the 1831 Co Derry census for anyone of the name Denning/Denin and variant spellings but without success, though there was a family living in Inshaleen, parish of Errigle in 1869.
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1869/11407/8189142.pdf
A death in Desertoghill parish:
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1882/06406/4839661.pdf
Another marriage, in Aghadowey:
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1879/11079/8054415.pdf
That was about it.
Possibly DNA testing may be a way of matching with others who have additional information about where the family originate. Family Tree DNA reportedly has more people with Ulster roots than any other company. That obviously increases the chances of finding a match. You might want to try them or, if you have already tested, you can transfer your results to them for no fee.
The North of Ireland Family History Society is running an Ulster DNA project in conjunction with FTDNA and can offer testing kits at a reduced price. http://www.nifhs.org (Go to DNA project on the website).
