Hello,
I am almost certain that Thomas Corlett, James' father died between April and September 1823, as James is said to be a posthumous child.
There is a burial for a Thomas Corlett at Ballaugh during this time period. Also, a will listed in Brian Lawson's index for Thomas Corlett of Ballaugh in 1823.
You can look at these records by going to your local LDS (Mormon) family history center, and ordering the films below. They will be sent from Salt Lake City, and available for your viewing at the center for a period of about one month. The rental fee is nominal.
Burial: LDS film 0106707
Will: LDS film 0206424