There are 3 people named King in Fintona in the current phone book. Search under BT78 as the address. http://www.ukphonebook.com
Fintona Presbyterian Church records start in 1836. There?s a copy in PRONI (the public record office) in Belfast, and they are on the Rootsireland site (pay to view) where there are 12 baptisms and 7 marriages listed, involving people of that surname. (Search under the country genealogy option, and you can narrow the search to specific churches).
http://tyrone.rootsireland.ie/search.php
Griffiths Valuation for 1860 lists 4 King households in Cumber. Archibald with a farm and 68 acres (plot 1); James senior with a farm and 55 acres (plot 2); James jnr with a farm and 32 acres (plot 3) and Eliza with a farm and 33 acres (plot 4). All are off the modern Cavan Rd, a minor road off the B46, half a mile or so from Fintona.
A couple of probate file abstracts:
Full Abstract :
Administration of the Estate of Mary Anne King late of Ganvaghan Knutsford Drive Cliftonville Belfast Widow who died 12 December 1912 at Cumber Fintona County Tyrone granted at Belfast to John Alexander King Hardware Merchant.
Full Abstract :
King Richard of Cumber Fintona county Tyrone farmer died 24 December 1916 Probate Londonderry 14 September to Robert King shop manager. Effects ?282.
The files for the 2 abstracts are held in PRONI. They are not on-line.
Looking at the revaluation records, the King family seem to have disposed of the last of the 4 properties in Cumber in 1929, when Thomas King on plot 4, sold to a Mr Woods. It doesn?t appear there are any Kings farming there now. You may get some addresses from the 2 probate files.