Registering change of ownership has only been obligatory in Ireland (both the Republic and Northern Ireland) since the 1990s. Prior to that, you mostly just needed to hang on to the deeds to prove ownership, though there was an option to register transactions with the Registry of Deeds in Dublin. There was a fee attached to that so many never bothered.
Second point is that the vast majority of the population didn’t own their properties in Ireland. Most just rented because landowners wouldn't sell (a source of great discontent with farmers). So they had leases, in some cases lengthy ones, but not ownership. That changed a bit with Wyndham’s Land Act in 1903 but prior to that only a minor proportion of the population owned their property.
It might be easier to help you if you were specific about which property/land you are interested in, and when.