Dunluce and Billy are separate parishes of ancient origin and cover the western and eastern banks of the river Bush respectively. As the river flows through the town of Bushmills, half the town is in each parish. The presbyterian congregation of "Bushmills" was originally called Billy and was founded in the centre of that parish in 1692. However in 1702, the original church being unable to meet the needs of that congregation, "temporary" permission was granted by the Presbytery for the congregation to use a building in the town of Bushmills (and which happened to be in the parish of Dunluce!). When the "temporary" church was in bad repair in 1746, a new church was built in the town of Bushmills but back on the eastern (Billy) side of the river. About a third of the members wished to remain in the old church (which they fixed up) and in 1754 they received recognition as a separate congregation, called "Dunluce".
It is possible that a family living in Billy parish would have joined the Dunluce "breakaway" (e.g. preferred their minister/family ties), but I would have thought it more likely they would have remained with the original Billy congregation (now called Bushmills).
So, it's not a case of Dunluce (presbyterian) church being in Billy parish in the 1850s, but rather that Billy (presbyterian) church was in Dunluce parish until the 1750s!
Hope this helps.
