My dad was always proud of his Scottish heritage, so I never told him that I had uncovered the fact that although his grandmother was born in Scotland, she was actually the daughter of Irish parents.
Her US death certificate names her birthplace as Lanarkshire Scotland in 1874, but I've not been able to locate a Scottish birth, christening or census record for her.

Can anyone direct me to sources for records of Irish Catholic migrants in Scotland?

Thank you.