Since my original reply to this posting, I have found the following information which could fit into your time period.
My paternal great grandparents were HENRY McKERNAN (as shown on the Tithe Applotment records)/ McKIERNAN and SARAH McCAIGUE/McCAUGUE. Some kind soul in the UK sent me some information he found on my family in UK records, while he was researching his family.
James b. 1839
Isabella b. 1842
Henry b. 1844
Charles b. 1847
I also found a descendant of another daughter, Mary. Mary's estimated year of birth is 1840. This Mary had a daughter named Mary Ann.
Their father, HENRY McKERNAN/McKIERNAN mentioned above is listed as being on the townland of Turnaroan, in Culfeightrin RC Parish, Co. Antrim, in the year of 1831. This HENRY and SARAH, as far as I know, are also buried in the same cemetery, as the HENRY and SARAH mentioned in my original reply.
One of my father's many siblings was also a Sarah.
The year of 1836 would fit into this time. Unfortunately, I do not have access to UK records to find the other siblings of my grandfather, Charles. The UK records I seek, for whatever reason, were not filmed by the LDS and I don't see any trip to Ireland in my future. So I'm still hoping there are other McKERNANs/McKIERNANs researchers out there who belong to my Co. Antrim line. (Or those who might have any connections to my Co. Leitrim line, siblings of my maternal grandfather, of the same surname name.)