The vast majority of land was rented, not owned outright. (The reluctance of landowners to sell, leaving 90% of the land owned by 10% of the population, was one of the major social issues for hundreds of years in Ireland).
Most farms were leased. At the top end of the scale, in the 1700s there were 3 lives leases which meant just that, the land was yours for the duration of the 3 people named in the lease, which might get you 50 or 70 years tenure. At the other end of the scale might be leases for 5 or 10 years or “at will” where no notice was required at all. Some of the longer leases were registered in the Registry of Deeds in Dublin. Copies – called memorials - were noted in the Registry’s records (and can still be seen and searched there). Duplicate copies for all of Ireland are also held by PRONI in Belfast. However many shorter leases were not registered at all.
Where you see land apparently being left to children etc in wills, in most cases what was being left was the unexpired portion of the lease, not outright ownership.
Where land was sold, there was no requirement to register the transaction either, though increasingly they were registered. (Compulsory land registration was only introduced in Northern Ireland in about 2002. Not sure about the Republic of Ireland but suspect it wasn’t too different). If you think land was sold, you can try the Land Registry but do not be too surprised if they have no record of the transaction, if it was in the 1800s.
Griffiths Valuation can tell you whether land was owned or rented. In general, where land was owned outright, it was recorded as “in fee” in the column for immediate lessors. (You may also occasionally see the term “free” used. This usually meant the person was squatting and didn’t in fact own the land/property at all).