Nineteenth century vital (birth, marriage, death) records are usually not a source that can give the Irish place of origin. Exceptions abound, but their main value is providing the names of parents, if that question is asked on the record and if the answer is known. With that in mind, any state vital record set that has a larger than normal amount of records with an Irish place of origin is to be welcomed and highlighted.
One such set of records is Wisconsin, Death Records, 1867-1907 on Familyserach.org (there is also a record set on Ancestry.com, Wisconsin Deaths, 1820-1907, but this does not seem to contain the same level of information for Irish entries). In total, there are c.33,700 records that list Ireland as the place of birth (the total number of records in this database is 432,959). About 3.75% of the Irish entries give a county or town of birth.
Small numbers, but a probably larger percentage than will be found in other state vital record sets of the same era. The county breakdown is as follows (grouped by Irish province):
Tipperary 51 Cork 223 Kerry 49 Waterford 65
Clare 79 Limerick c.75
Galway 70 Mayo 72 Sligo 75 Roscommon 28
Donegal 16 Antrim 42 Armagh 2 Derry 12
Down 29 Fermanagh 1 Tyrone 20 Cavan 32
Dublin 136 Wexford 20 Kilkenny 40 Carlow 10
Louth 10 Wicklow 22 Kildare 1 Meath 28
Offaly 34 Laois 24 Westmeath 9 Longford 27
Dublin and Cork lead the way, probably reflecting emigration from the county with the largest population in Ireland (Dublin) and the county that has traditionally had one of the largest numbers of emigrants (Cork). Other prominent counties in the database are from the western seaboard: Clare, Galway, Mayo, and Sligo, again counties with traditionally large emigration numbers.
The record set contains some interesting and very valuable examples. In the entry for Ellen Kerin Scanlan, she is listed as born in Ennistimen (Ennistymon), Co. Clare, about 1830. Her spouse, religious affiliation, and parents (including their place of birth) are also named. Catholic Church records for Ennistymon parish begin in 1823, so if this is your ancestor you would hopefully be able to find a corroborating baptismal entry (assuming that the listing of Ennistymon was not just an approximation of where she was born in Clare, when in fact she was from a neighboring parish!)
 Wisconsin, Death Records, 1867-1907. Index. FamilySearch. http://www.familysearch.org : accessed 2014. Citing Wisconsin State Historical Society, Madison, Wisconsin.