Just heading out, maybe the following will provide a lead. The 1902 marriage of Thompson Keys to Martha Robinson in Clogher Church of Ireland looks sound because in the civil record, apart from the groom's distinctive name, he was recorded as a carpenter living in Findermore. The bride was recorded as living in the townland of Mullaghtinny and importantly, her father was given as 'not known'.
(to complete the information, the groom's father was also called Thompson Keys - a labourer - and the witnesses were George McLelland and Maria Leslie)
This may well have been Martha in 1901 under the surname Keys:
http://www.census.nationalarchives.ie/pages/1901/Tyrone/Aghintain/Lislane/1726629/However, there were Keys in Mullaghtinny in the 1901 census (Fleming and Rhoda Keys and family), maybe related:
http://www.census.nationalarchives.ie/pages/1901/Tyrone/Clogher/Mullaghtinny/1726117/In terms of geography, Mullaghtinny is the area immediately east of Clogher village, the townlands of Findermore and Aghintain lie to the other side, about 1.5 miles SW and 2.5 miles W respectively.
Finally, note that a Martha Jane Robinson was born in Clogher Workhouse on 20 August 1878, father unknown, mother given as Rhoda Robinson. Rhoda isn't / wasn't a hugely common forename in Ireland... it all raises some interesting possibilities.
Edited to add: Someone also called Rhoda Robinson, living in Killygordon, had a daughter Elizabeth on 29 April 1876, again the father was unknown. And in relation to Fleming and Rhoda Keys in the 1901 census, while I can't yet find a marriage, there were births registered in Omagh to potentially fit children William and John - the mother's maiden name was Robinson (available online via GRONI website) .
Rhoda Keys and sons in 1911:
http://www.census.nationalarchives.ie/pages/1911/Tyrone/Cloghan/Mullaghtinny/855919/