This information from Ulsterheart may help:
p. 301 "John Hamilton, probably a son of David Hamilton who was a Stewart tenant in Cooligery in 1856 was probably a descendant of the John Hamilton of Millex whose name is enshrined in Kerog porch."
Many families in the Ballygawley area had several leases-- one listed as house, office & land, their primary residence, and another usually nearby lease of land only to extend their farming land.
The land in Coolageery would have been fairly close to David Hamilton's property on Meeting House Street in Ballygawley. He probably had a business based at that Ballygawley town location.
You may find more information about David Hamilton's family by looking up the Valuation Revision records for his leases on Proni, searchable by townland and parcel number.
http://apps.proni.gov.uk/Val12B/Search.aspxIt is also helpful to look at the maps on
http://www.askaboutireland.ie/griffith-valuation/.
I have a Mary Hamilton born pre-1800, married to Mark Patterson of Killymorgan townland, Errigal Keerogue parish, Tyrone. Still trying to determine who her parents are. James Hamilton of Millix townland, Errigal Keerogue is the best candidate so far.