I don't have much information on the McIlveens. I have a chart given to me years ago that has 3 members of the Lowe family marrying McIlveens.
My grt grt grandmother Catherine Quinn 1835-1909 was the daughter of Michael Quinn(mothers name not given) he is listed as the son of Stephen Quinn and Mary Hand, Stephens parents were Terrence Quinn and Catherine Laughlin. I do not have an Elizabeth among the names on my chart. But there were a lot of Quinns in Cullyhanna she may be a cousin. If I find anything I will let you know.