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see fifth record for james in 1871 https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1871/03281/2202159.pdf They lived in Clooncan townland Robeen civil parish. James had an older brother William 1869 Francis and Honor 1873 Thomas 1875 Catherine 1877 Stephen 1880
fourth record for marriage of Michael and Mary and as you indicated Michael was a widower https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1869/11413/8191512.pdf
I found a March 25 1858 baptismal record for a John Gibbons with parents Michael Gibbons and Ellen Burke from Clooncan. There was also a Patrick baptized January 1 1860.
Records for the parish start in October 1857. I was not able to locate a marriage record so presumably the marriage occurred before October 1857.