Hi John,
Roman Catholic parish records are probably your best source. They generally go back to the early 1800s,though some parishes have gaps and incomplete records. These are available on the subscription site www.rootsireland.ie and also for free on www.findmypast.ie, though I find roots Ireland to be the most complete. These parish records contain baptism and marriage records. A good piece of information is that they provide godparents and witnesses names, who were often relatives or neighbour's.
The Tithe Applotment Books are available on www.nationalarchives.ie. They are from the 1820s and 1830s. Back then, anyone with enough land of rateable value paid a tithe for the upkeep of the Church of Ireland, even if they were Catholic. The name of the landowner, the amount of land they owned, and the amount of their rent and tithes were recorded. If your ancestor does not appear on this though, it could be because they did not own enough land to pay a tithe.
The Flax Growers List 1797 provides sparse information but if you know the area your family would have lived around then, you might be able to find them. Back then the Irish Linen Board were trying to encourage people to plant to boost linen production and offered them free looms and spinning wheels as a reward. They made a list of all the farmers who signed up. It gives names and where they came from. This can be found on the free site www.failteromhat.ie
Irish Poverty Relief Loans can be found on www.findmypast.ie and are records of small loans poorer people took out during the 1840s. They provide the names of people, whet re they lived, the amount of the loan and the witnesses.
Hope some of this helps!
Alicia
