Thank you so much for your help!
Marriage - Luke Doherty was married in the US to an American woman in rural South Carolina. I have not been able to find any marriage certs for them, as they probably do not exist. That was before they were required to keep such legal documents, and many pre-Civil War documents were lost in that area due to fires, and war. I have not tried contacting the Catholic diocese in the area to see if they have any records from the marriage yet, but I have checked with LDS and they don't seem to have anything either.
Naturalization - I have found no records of passenger lists that I can say with certainty "this is him". I was able to find a document from Charleston city court that he filed a notice of intention on December 17, 1850. However, it's just a list of county records there is no additional information provided. I just learned that LDS has some of South Carolina's naturalization records on microfilm and plan on visiting their facility to see if I can find it there.
Death cert - again, unfortunately this was prior to the requirement of official records keeping. So all I have been able to find is a handwritten note, stamped with a file number that is from his treating physician explaining the cause of death, date, and the seal of the cemetery where he is buried. I have looked at most of his childrens' death certificates and they simply say father's place of birth "Ireland" or "County Mayo, Ireland".
Other than that, I think I'm just plain stuck. I know a lot about this man's life in the US, but nothing of his life or family in Ireland. It may be possible that while Mr. Doherty's birthplace is County Mayo, he may have lived elsewhere in a different county as an adult prior to immigrating to the US.
Thanks so much for your help, I truly appreciate it! I will broaden my search to include Luke Doherty in other counties and see if anything turns up, as well as checking with LDS on the naturalization records.