I located seven siblings to Peter: Bridget 1857 Edward 1861 John 1862 Martin 1864 Matthew 1867 Honor 1873 Mary 1877 Records located on the subscription site Roots Ireland.
Killala marriage records start in 1873 and civil registration started in 1864. With a child born in 1857, John and Anne were likely married in 1856 or earlier so no record would be available. Also no baptismal records would exist for John Cunningham and Anne Dooher since Killala baptismal records start in 1852.
The family lived in the town of Killala. No way to tell where they lived. John Cunningham was a labourer based on info on a birth certificate.
I don't see the family in the 1901 census in Killala. Did they emigrate?