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 W(illiam Maxwell M 1857 +/- 4 yrs, Cavan or Longford, I found 2 rcds: both in 1853 Cavan. One of these MAY show a bride named Mary. Caution - Mary is the forename of abt 20% of Irish females; its easy to grab a false positive. You can validate the rcd via discovering the parents' names on William's B rcd and comparing.
For W(illiam) Maxwell B 1832 +/- 4 yrs, somewhere in Ireland, with the father's forename unknown, I found 16 rcds: 1828 Derry, 1829 Cavan, 1829 Antrim, 1829 Roscommon, 1830 Dublin, 1831 Westmeath, 1831 Sligo, 1832 Cavan, 1833 Mayo, 1833 Dublin, 1834 Westmeath, 1834 Roscommon, 1835 Antrim, 1834 Galway, 1836 Antrim, and 1836 Donegal.
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.