Cannings of Garvagh, Londonderry (James and Helen)

I am researching my mother's paternal line which is the Canning name. My grandfather was first generation American born of Ulster-Scots parents both from the Garvagh area of Londonderry (William Canning and Sarah Jane Young) They were married in Aghadowey. William Canning (born about 1842 in Kirkcolm Scotland) was the son of James Canning (born about 1809) and Helen (sometimes Ellen, sometimes Elinar) Cook (sometimes McCook) who are both buried at St. Paul's church in Garvagh with their daughter, Mary Jane Hagan and her husband John Hagan.

My problem is finding siblings for James and his parents. From what I know, Canning is really an English name so this family was probably an Ulster plantation implant. I know that the Canning name is big in Garvagh as it was the Cannings that formed Garvagh but I have not been able to make any connection to those Cannings who were quite wealthy, as my great-great grandfather was just a tenant farmer for the Church of Ireland.

We have had our DNA done through Family Tree DNA and through Oxford Ancestry and we are J2 haplogroup which is rare for Britian except more are found in England than anywhere else in that region. We have come up with a DNA match to the McKinney family (whose ancestor was also a William Canning around the 1600's) and family of Kenning in California who originally came down from Canada.

Any leads or ideas are very welcome!