Kevin:
Roots Ireland www.rootsireland.ie has Annaghdown RC records starting in 1834. I was not able to locate James so he may have been born just before the records started. I did locate an index record for Cecelia (or variant) in Annaghdown in 1838. Parents were Michael and Honor Devaney. There are three other children born to a Michael and Honor Devaney (or variant) in Co. Galway West. Without the name of the child Roots does not let you search the individual parish records e.g. Annaghdown. Possible they relate to another family.
Roots is a pay site to view a transcription of a church record.
I also looked at the 1856 Griffiths Valuation head of household listing for Annaghdown parish.
http://www.failteromhat.com/griffiths/galway/annaghdown.htm
They may have been deceased or left the area by 1856. There were a number of Grealy entries in the parish.
Roger McDonnell