I research the Irish Family History Foundation's database. It contains 12,800,000 surviving rcds for abt 70% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800. Cos. Donegal and Derry were recently added to the database.
Note 1 - Without a KNOWN county, the chance of an ancestor's rcds NOT being in this database is AT LEAST 30%.
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).
Note 4 - Microfilms of parish church rcds are kept by the National Library of Ireland (NLI).
For Mic(hael) Madden B 1815 +/- 15 yrs, Co. Limerick, with a father forenamed Mic(hael), I found 17 rcds: 1810 Knockainy & Patrickswell, 1812 Solohead & Oola, 1812 Fedamore, 1816 Mahoonagh, 1818 Pallasgrean & Templebredon, 1818 St. Patrick's, 1819 Murroe & Boher, 1820 St. Munchin's, 1820 St. Mary's, 1824 Knocklong & Glenbrohane, 1824 Shanagolden, 1825 Hospital & Herbertstown, 1825 St. Patrick's, 1827 Solohead & Oola, 1829 St. Munchin's, 1830 Ballybricken & Bohermore, and 1830 St. Munchin's RC parishes.
For Mic(hael) Madden Sr M ditto, I found 6 rcds: 1811 Pallasgreen & Templebredon, 1816 Hosptial & Herbertstown, 1818 St. Mary's, 1824 Fedamore, 1828 St. John's, and 1829 St. Mary's RC parishes.
For Pat(rick) Duggan M 1815 +/- 15 yrs, Co. Limerick, I found 3 rcds: 1809, 1818, and 1830.
For Maria Hayes M ditto, I found 19 rcds - too many to easily summarize here. Will leave this picking and matching task to you.
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.