Unfortunately, the official recordkeeping for births did not occur in Ireland until 1864. Marriages began in 1845. You will need to figure out from which parish they were from and search through the relevant parish records.
You may find that they came from the same place -- Co. Armagh and Co. Tyrone border each other, and as is the case in my own research, because they lived close to the border, the parish records for them exist in both places; ie, baptized in one church in Co. Armagh and married in another in Co. Tyrone, but they never moved.
The 1870 census shows Wilson living with his wife and children, along with William and also a Margaret, aged 37, who is likely another sibling.