Kerry,
I think the correct spelling of Lisnabable is Lisnarable. It’s a rural townland of 341 acres. There were 18 farms there according to Griffiths Valuation, in 1860. The only Rafferty household was plot 14 which was headed by Cornelius Rafferty who has a 20 acre farm. I suspect that may be one of your families. The farm today is up a lane off the Eskragh Rd BT70, near the “Playtime Day nursery”. There’s an RC church close by which is presumably where your family would have attended. The general location is about half way between Clogher and Omagh. Perhaps 8 or 9 miles north of Clogher.
http://www.askaboutireland.ie/griffith-valuation/index.xml?action=nameSearch
I don’t see anywhere in the area named Burnhill.
Here’s the Lisnarable farm in the 1901 census:
http://www.census.nationalarchives.ie/pages/1901/Tyrone/Cecil/Lisnaiabee/1725883/
And in 1911, the son in law has taken over the farm:
http://www.census.nationalarchives.ie/pages/1911/Tyrone/Cecil/Lisnarable/855688/
I noted this probate abstract (summary) from the PRONI wills site, which tells you there were still descendants on the farm in the 1930s:
Gorman Mary Jane of Lisnarable county Tyrone died 1 March 1932 Administration Londonderry 17 December to James Gorman farmer the husband. Effects £43.
Looking at the revaluation records, the farm passed from Cornelius to Joseph in 1872. So Cornelius probably died around then. Checking the GRONI death records reveals Cornelius died on 28.3.1874 aged 75. Death registered in Clogher. You can view the original certificate on-line on the GRONI website, using the “search registrations” option:
https://geni.nidirect.gov.uk
You will need to open an account and buy some credits. It costs £2.50 (sterling) to a view a certificate.
If you google “photos of Clogher” you’ll get some but it’s not actually where your ancestors lived. They lived in the country nearby and Clogher was just where the local Registrar lived and perhaps where they went to conduct business.
