If there was ever a one-stop-shop in genealogy, it would be ScotlandsPeople: www.scotlandspeople.gov.uk Here you will find scores of Irish immigrants. The primary sources we all used on microfilm in years past has now been indexed, scanned and available online for a fee at this website. ScotlandsPeople has developed into one of the largest online sources of original genealogical information with about 90 million records on this government website.
The major collections which affect your immigrants from Ireland to Scotland would include the 1841-1911 censuses. The website has indexes to the government recording of births, marriages and deaths from 1855 through 2009. More recent images are scanned due to right-of-privacy concerns. A major collection from which to document Irish Catholics is the index and scanned images to the Catholic parish registers. This includes births/baptisms, banns/marriages, deaths/burials, communicants, confessions, confirmations, seat rents, sick calls and Status Animarum (a census).
ScotlandsPeople also has an index and scanned images to the Old Parish Registers (OPR) which are the records of the main Church of Scotland (Presbyterian). Because this was the state religion, persons of all faiths can be found in its records, so don’t neglect it as a source for non-conformist research. This includes Irish Catholics also.
Other important collections include an index and the images to the wills and testaments from 1500-1901. Then there is the Coat of Arms indexes which is the “Public Register of All Arms and Bearings in Scotland 1672-1907.”
More keeps being added to ScotlandsPeople so you need to constantly refer back to the website. This website is among one of the best I have ever used. As a genealogist, I use it constantly, and I have no difficulty recommending it! Don’t forget to check out the link to the sister website ScotlandsPeople – The Center: www.scotlandspeoplehub.gov.uk