The Stonebridge Presbyterian congregation was established in 1700, with its first minister being Rev. Patrick Dunlop, and its second, Rev. Archibald Meharg. Rev. William White next ministered to the congregation, serving for over five decades, from 1820 to 1874. The associated meeting house (church) and burial ground date to the founding years of the congregation. Many of the early graves are unmarked, or have slabs now covered by turf, with only depressions in the earth to show burial locations. Although most Stonebridge Presbyterian members were buried in the adjacent church cemetery, some were buried in the Clones Church of Ireland graveyard, a short distance away in the village of Clones.

The existing Stonebridge church is a free-standing gable-fronted building with a later single-storey addition to east. The church was built about 1830, on the site of an earlier structure, in the townland of Gransha More in Clones parish, County Monaghan. A date plaque on the gable is inscribed "1700" -- referring to an earlier church building and the congregation's formation date. Local records show that a "new" or expanded Presbyterian Meeting house was built at Stonebridge in the early 1790s, probably the structure that was replaced about 1830, with the date plaque reinstalled from building to building over the decades.

In "A Topographical Dictionary of Ireland" (1837), Samuel Lewis wrote: "There is a Presbyterian meeting-house at Stonebridge, in connection with the Synod of Ulster." Of the village, he described: "...at Stonebridge is an extensive foundry for spades, ploughs, and other agricultural implements, established about ten years since." Stonebridge village in the 19th century consisted of a small church, a school, a mill house and several homes, centered around an arched stone bridge across the River Finn, which gave the village its name.