Jon,on rootsireland.ie there are two births for John and 2 for Henry.
birth John McCormack: 1853 John Henry McCormack co Antrim 1859 John James McCormack co Antrim
birth Henry McCormack: 1853 Henry John McCormack co Antrim 1865 Henry McCormack co Antrim
The only thing is that these records are not coming up in the Catholic parishes nor do they have the mother's name on them.You would have to decide which you think belong to your family.
I did find this marriage which may help; marriage 19 July 1858 parish:Antrim co Antrim church:Randalstown Roman Catholic Rev J.Lennon Henry McCormack Roman Catholic Ellen McCann Roman Catholic witnesses:John Mitchell Catherine Mitchell
If these are you family then I'd say the 1859 birth for John and the 1865 birth for Henry would be the correct ones.Hope this helps,Kim