I searched the subscription site Roots Ireland and did not find a marriage record for John Shine and Jennue Cox. Castletownroche/Ballyhooley records start in 1811 https://registers.nli.ie/parishes/0031 so either they were married befoe 1811 or in another parish that does not have records back to the 1810s. I did find two baptismal records William Shine baptized September 3 1815 (mother Jennifer Cox and Bridget Shine baptized January 13 1825 (mother shown as Jane Cox).
Roots Ireland did not have a record for James but I went on the register and found the very faint record for James. It is record 285 and the next to last record in December 1818, https://registers.nli.ie/registers/vtls000632864#page/55/mode/1up Based on the condition of the register, there are likely other children besides James, Bridget and William.
The family lived in Balyyadeen townland in Castletownroche civil parish.