If the marriage of John and Bridget McDermott took place c1840 then you are dependant upon church record of the marriage (which may not survive) so I'm not sure what you mean by "I have searched all Ireland records and but I have not cross referenced a Bridget Cairney(Carney,\ Kearney) to any McDermott."
Carney/Kearney, etc. found all over Ireland and it could be that what looks like 'Cairney' in the U.S. marriage record is a variation of Carney.
Most U.S. state death records ask for details of birthplace and date, parents' names, etc. Is it that the information is not on Michael McDermott's death certificate (perhaps the informant didn't know) or that the details were not on the form?