Hi Vic
Prior to 1864 and civil registration of births in Ireland you will have to rely on church registers to confirm birth details of Patrick Collins, son of Patrick Collins and Mary King, born 1852 in Ireland and Anne/a Haley born 1855 possibly in Ireland. Dates of commencement and quality of information in church registers vary from parish to parish and from denomination to denomination. Access to church registers, in the absence of indexes and databases, is generally gained through knowledge of an ancestor's parish address and religious denomination.
There is no national index to Irish church registers. To date, only the county-based genealogy centres have attempted any large scale, systematic indexing of church registers in their localities. Although RootsIreland, at
http://www.rootsireland.ie, is the largest online source of Irish church register transcripts, it must be emphasised that a failure to find relevant birth/
marriage entries in this database doesn't mean that the events you are looking for didn't happen in Ireland. It simply means that they are not recorded in the database; for example, they may be recorded in a record source which doesn't survive for the time period of interest or in a source that has not been computerised.
It is fair to say that to visit the ancestral homeland in Ireland and/or select record sources to search you really need to know the parish they came from. The Province of Munster, which consists of counties of Clare, Cork, Kerry, Limerick, Tipperary and Waterford, was subdivided into 786 parishes!
If you are unable to identify relevant information in the RootsIreland database,
http://www.rootsireland.ie, (or any of the ‘big’ Irish databases such as
http://www.irishgenealogy.ie and
http://www.findmypast.ie) or, indeed, in other sources then, unfortunately, you hold no specific clues to guide you as to where in Ireland you should concentrate your research. If you cannot find your ancestor in any of the significant Irish databases then you will have to conduct your own research through archives. It must be said, however, that this is only a realistic option if you know the county and parish your ancestor lived in Ireland.
If you hold no clues as to where in Ireland your ancestor came from you could perhaps consider doing further research through record sources in the US (such as
marriage records, census returns, death notices) and with family contacts to see if you can identify any clues as to the county and parish of origin of your Irish ancestors.