Michael D Dunagan : Short Biography

My irish ancestor is Michael Dunagan (spelled a variey of ways).  He first shows up in a record in the Town of Hunter, Greene County, New York, USA in the 1830 Federal Census with a wife and two young daughters.  From various sources it is known he was born in Ireland in about 1804 and he was probably in the United States by 1825, perhaps a bit earlier.  No record has been found in the USA  telling where he was from, when he came to America, who his parents were, or whether he had siblings.  In America, he married a wife with long roots to the new country - Eleanor Underhill (primarily English roots).  Family lore is that Michael was from County Cork, possibly from near Cork City - but thus far there is no evidence.  If he followed a typical naming pattern, for his children, his eldest son was John Henry Dunagan so perhaps his father was John or Henry or John Henry.  Other sons were 2. Andrew, 3. Michael and 4. William A.  Daughters were 1. (Eldest daughter unknown) 2. Mary Ann, 3. Ellen Elizabeth, 4. Lucy C., 5. Martha Jane, 6. Julia Theresa. [The names William and Martha are the names of wife Eleanor's parents.]  Michael died between 1851 and 1854.  When his wife died in 1891 she was lised as Mrs. M.D.Dunagan, so perhaps Michael's middle name began with 'D' (Daniel?, David?). I have found a few Michael Dunagan's in the Irish records, but so far none fit timing (early 1800s) + location (Cork) + naming paterns to make me believe I have found my guy.