The parish will be Tyrella. It's close to Downpatrick.
2 Hanna farms there in the tithe applotment records for 1834:
http://www.irishgenealogyhub.com/down/tithe-applotment-books/tyrella-parish.php
Griffiths Valuation for 1863 has 4 Hanna households in Tyrella. All were in the townland of Clanmaghery.
http://www.askaboutireland.ie/griffith-valuation/index.xml?action=nameS…
There are 8 probate files on the PRONI wills site relating to Hanna of Clanmaghery. For example:
The Will of Robert Hanna late of Ballyvastin in the County of Down Farmer and Carpenter deceased who died 22 February 1864 at same place was proved at Belfast by the oaths of Patrick Hanna Senior and Patrick Hanna Junior both of Clanmaghery (Clough) in the County of Down Farmers the Executors.
The Will of Patrick Hanna late of Clanmaghery County Down Farmer who died 2 December 1887 at same place was proved at Belfast by John Hanna of Clanmaghery Farmer and Patrick Smyth (Senior) of Carricknab said County Spirit Merchant the Executors.
https://www.nidirect.gov.uk/services/search-will-calendars
1901 census:
http://www.census.nationalarchives.ie/pages/1901/Down/Tyrella/Clonmaghery/1229659/
http://www.census.nationalarchives.ie/pages/1901/Down/Tyrella/Clonmaghery/1229678/
http://www.census.nationalarchives.ie/pages/1901/Down/Tyrella/Clonmaghe…
