Okay, I have found John and Mary (Lowry) Farrell's marriage record along with their son, Michael's, baptismal record, his wife's, Margaret Brien (O'Brien), and their daughter, Bridget's, baptismal records. I post the last three records above on this thread.
Church Marriage Record
Marriage: 02-Feb-1823
Parish : TYNAGH, County Galway, Roman Catholic
Husband : John Farrell (father Farrell)
Wife: Mary Lowry (father Lowry)
Witnesses: William Farrell and Biddy Mulkern
Children of John & Mary Lowry Farrell
Thomas Farrell 1823 Tynagh (RC), Co. Galway
Bridget Farrell 1825 Tynagh (RC), Co. Galway
Patrick Farrell 1828 Tynagh (RC), Co. Galway
John Farrell 1829 Tynagh (RC), Co. Galway
Mary Farrell 1831 Tynagh (RC), Co. Galway
Michael Farrell 1833 Tynagh (RC), Co. Galway
Peter Farrell 1835 Tynagh (RC), Co. Galway