Hi,
You are lucky having such a rare name to research. There were 6 Tarlton households in the Griffiths Valuation in Antrim, Dublin, Fermanagh and Galway and 23 Tarleton mainly around Offaly and Laois.
http://scripts.ireland.com/ancestor/surname/index.cfmLaois used to be called the Queens County and Offlay the Kings County.
Write down exactly what you know from birth, marriage etc records first so you know what you know and what the source is. Then you can see what holes you are left with.
This is probably one of yours from the Griffiths Valuation in Co Kildare in 1851.
Tarleton Weldon Oldcourt Kilberry Kildare
There's also
Tarleton John Ballaghmore Stradbally Laois
Tarleton John Carricksallagh Stradbally Laois
Tarleton John Kylebeg Stradbally Laois
Tarleton John Oughaval Stradbally Laois
Tarleton John Stradbally (Main Street) Stradbally Laois
Tarleton Rev. Jno R. Tullylish Tehallan Monaghan
Tarleton Rev. John R. Templetate Tehallan Monaghan
Tarleton Rev. John R. Tuckmilltate Tehallan Monaghan
Tarleton Rev. John R. Tullygony Tehallan Monaghan