Carmen, many of the famine-era Irish settlers of Jennings County, Indiana, were from the Roman Catholic parish of Ballycroy (and surrounding area) in County Mayo, Ireland. Many of them -- including your McGintys and my own Lanahan ancestors -- migrated from there to Jennings County via Canada and through New York. Ballycroy is in a wildly beautiful part of Ireland and I encourage you to visit it. The church records, however, don't go beyond the 1890s and there is little available locally that will help you trace your ancestors.
A web search for McGinty and Ballycroy will turn up quite a bit on this family.
The National Archives of Canada has made many of their immigration records available for online searching. See http://www.inGeneas.com/free/index.htmlhttp://www.inGeneas.com/free/index.html. My Anthony and Selia Lenehan (Anthony and Celia Lanahan) from Ballycroy-- who ended up in Jennings County in 1851 arrived in Quebec aboard the Britannia in 1842. Three McGintys -- Anthony, Bess, and Honor -- were on the same ship.
These families were members at first of St. Catherine's Church in Jennings County, which is now extinct, and later were members of St. Mary's in North Vernon. Records of both churches are available on microfilm from the Family History Library. (See http://www.familysearch.com/.http://www.familysearch.com/.)