Jack:
I located the marriage record for the parents and birth records for three children including Michael.
first record 1875 marriage record names of fathers shown https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_ret...
second record 1877 for Denis https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_return...
fourth record 1879 Margaret https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_return...
last record for Michael 1883 https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_return...
Michael Carey Sr. died in 1888 https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_retur...
Mary Carey is not in the 1901 census in Curragh but I was not able to find a death record.
1901 census just Denis in Curragh http://www.census.nationalarchives.ie/pages/1901/Limerick/Mahoonagh/Curr...
1911 census Denis married with children http://www.census.nationalarchives.ie/pages/1911/Limerick/Mahoonagh/Curr...
Let me know if you have any questions.
Roger McDonnell