A great source on this line (and the Bates line as well) is the book "The Meighen Sept in America and in Ireland" by Bernard Patrick Meighenn (1979)--now out of print but if you want to find acopy I may be able to help you track one down.
Before I bought mine I was able to get it at my local library through interlibrary loan.
email me at firstname.lastname@example.org for more extensive information - according to this book your dates for Mary Ann Meighan are correct.
Her father John, the book says, was born in Ireland to James William Meehan (Meighen) and Susan McCloskey Meighen. John is said to have lived in Fayette County PA for a time with hisparents, and then to have moved to Ohio where he spent most of his life. There is a page in the book on John Meighen and on and Mary Ann's mother,John'swife Christena (maiden name not known).
John is buried in the M.E. Church Cemetery at Mt. Ephraim, Ohio, his grave marked by a five-foot high black stone momenument erected by his daughter Mary Ann Meighen. Christena was born in 1774 and died on Nov 26, 1846 and is buried in St. Mary's R.C. Church Cemetery in Temperanceville, Ohio.
The book says that Bethel Bates, son of Timothy Bates, and Mary Ann Meighen were married in 1831. There is about a page of information on Bethel Bates, who served in the state legislature. His parents were Timothy Bates born Nov 29, 1778, and Ruth Moore Bates; his grandparents (Timothy Bates's parents) were Ehpraim Bates, born May 24, 1774 at Morristown, New Jersey, and Susannah Bates (maiden name not known).
There is more background and info on the Bates family as well. Bethel Bates' younger brother, Timonty Jr. , also married aMeighen -- Sarah Jane Meighen, in 1843; Sarah Jane was Mary Ann's younger sister. See the book and/or email me for more info!