I research the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800.
Note 1 - Without a KNOWN county, the chance of an ancestor's rcds NOT being in this database is AT LEAST 35%.
Note 2 - Only 1/2 of Co. Cork's rcds are in this database.
Note 3 - The RC church kept control over most parish rcds from Tipperary (north). These are ONLY available thru the Tipperary Family History Research center at a substantial fee (regardless of outcome).
For Benjamin Dixon B 1842 +/- 1 yr in Co. Cavan with the father's forename unknown, I found 1 rcd in 1841, Drumgoon CI parish. The father's forename was James. This MAY be for your ancestor - no guarantee. A view of the detailed B rcd SHOULD show his parent's names. Note - There are only 4 other Benjamin Dixon (+variants) B rcds in all Ireland for all time: 1833 Antrim, 1852 Dublin, 1857 Cavan, and 1886 Antrim.
For James Dixon M 1838 +/- 4 yrs, Drumgoon parish, Co. Cavan, I found 1 rcd in 1840. This has an even chance of being for your ancestor's father. A view of the M rcd SHOULD show the bride's name and also their parents' names plus other info.
For siblings, the only other B rcd in Drumgoon with a father forenamed James is in 1828. This seems far too early for your timeline. Possibly he's an uncle.
Google the Foundation's name to lead you to this database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genforum msg.