Samuel Lewis's Topographical Dictionary of Ireland, Vol. I, p.151 lists : BALLYMORE, or TANDERAGEE, a parish in the barony of Lower Orior, county of ARMAGH, and province of ULSTER : containing, with the town of Tanderagee (Tandragee), the village of Clare"...etc. "Acton House of Conway R. Dobbs"..
The PRONI Freeholder's records (http://www.proni.gov.uk/ ) shows :
CLARE James Adair ARM/5/2/7 James Adair D/1928/F/26A
BALLYSHEALMORE (Ballyshiel More / Ballymore & Ballyshiel beg ) James Adair ARM/5/2/7 c.1812 lease for life of Alex Adair & Blevis ? Thomas Adair ARM/5/2/7 c. 1812 lease for life of Alex Adair & Blevis ? James Adair D/1928/F/26A Thomas Adair D/1928/F/26A
There may be more information at the PRONI site for above in the Freeholder's Records ?