Looking at the tithe applotment records for Dromore in 1834 there were 3 Close households in the townland of Balleny (David George & John). They were the only Close farms in the parish.
Looking at the 1901 census for the same townland I see about 5 or 6 Close households, all Church of Ireland.
So on the basis that your family were Church of Ireland and came from Dromore, have you tried searching the local church records for the 2 children’s baptisms in 1842 & 1847? You might also find the parents marriage there, but that’s only if the bride happened to attend that church. Tradition was to marry in the bride’s church after which she’d attend her husband’s. So they may have married elsewhere but you might expect the children to be baptised in Dromore Church of Ireland. You might also find Robert’s baptism c 1812 and any siblings. The baptism & marriage records start in 1784. Copy in PRONI in Belfast.