Hi there,
You already have done lots of research about your Babington family. This is great. It's even better that you are in touch with Babingtons here in Ireland. Two heads are better than one!
You may have already exhausted these avenues of research, but in case you haven't I will mention them here anyway.
There are Roman Catholic church records available for Magheracloone. These date from 1835 for baptismal records and 1827 for marriage records. Both only date until 1880. You can find these at the National Library of Ireland (NLI), Pos. 5574, or PRONI (Public Records of Northern Ireland) MIC.1D/17; C.R. 2/17. If you have any difficulty, you could try writing to the parish priest for more assistance.
Church of Ireland parish registers for the period up to 1870 are public records. Registers are available for about one third of the parishes, however many were destroyed in the Public Records Office in Dublin in 1922. Most are still held by the local clergy, although some are in the National Archives of Ireland and others are in the Representative Church Body Library in Dublin. A list of all surviving registers is available in the National Archives.
Civil registration records are available from the General Register Office (GRO). These start from 1864 however. You can access the website here: http://www.groireland.ie/research.htm
You could also try checking the land records called the Tithe Applotment Books (1823-38) or the later Griffith's Valuation (1848-64). Griffith's is freely available here: www.askaboutireland.com or here: www.failteromhat.com Failte Romhat has lots of other useful links you could try looking at.Tithe Applotment Books (1823-38). Microfilm copies of the books for all of Ireland are available at the National Archives of Ireland (NAI) http://www.nationalarchives.ie/genealogy1/genealogy-records/tithe-applotment-books-and-the-primary-griffith-valuation/ or the Church of Latter Day Saints (LDS).
Have you tried checking the Ellis Island records (www.ellisisland.org) or the Castle Garden records (www.castlegarden.org)? Generally, more information was given at the port of arrival rather than the port of departure. If you knew which city they arrived at, this could be a good place to find more information.
There is a useful link from The Irish Times which shows the predominance of a name in the country in the mid-19th Century. It also shows the variant spellings of the name which is useful when researching. You can also check the name in an area with another name, such as Babington and Leven. http://www.irishtimes.com/ancestor/surname/index.cfm?fuseaction=Go.&UserID= and http://www.irishtimes.com/ancestor/surname/index.cfm?fuseaction=Go.&UserID=
Have you looked at the records in Canada for more information about their immigration there?
1785 Male Protestants aged over 17 - Magheracloone & Errigak Trough. Church of Latter Day Saints (LDS), film 258517.
1796 Spinning Wheel Premium Lists. 4,400 names for Co. Monaghan. www.failteromhat.com
www.ulsterancestry.com
Gilsenan, M., Hills of Magheracloone 1884 1984, 1985.
Estate records: Landlord: Earl of Bath: NLI Pos. 5894. Rentals 1784-1809. Major tenants only.
Please make sure you link anyone else in your family who is interested in their Irish heritage to our site - and indeed anyone else you know of Irish heritage.
Kind regards,
Sinead Cooney
Genealogist (Ireland XO)