You don't mention the religious denomination for your ancestors but I will assume Roman Catholic. The subscription site Roots Ireland has baptismal records for that parish starting in 1830 and marriages in 1843. I searched for baptismal records for Hugh Tully with father Edward around 1820 and did not find a record. I looked for marriage records for Hugh Tully and the only record I found was a September 9 1852 marriage for a Hugh Tully to a Rose Smyth in the Killinkere RC parish. Likely not your Hugh Tully but I thought I would share the record.
So it appears that there are no RC church records for your ancestors.
The Ancestry records that your second cousin found are Tithe listings from the period 1828-1834.
Here is the 1828 record for the Edward Tully in Keenaugh who was leasing a little over six acres of land.
Let me know if you have questions.