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 James Dooley B 1845-1849 somewhere in Ireland with a father forenamed James, I found 5 rcds: 1845 Tipperary, 1845 Limerick, 2-1845 Antrim, 1849 Dublin, and 1849 Tipperary.
For James Dooley M 1840 +/- 4 yrs somewhere in Ireland, I found 20 rcds: 2-1836 KIL, 1837 LIM, 1838 KIL, 1838 TIP, 2-1840 LIM, 1840 OFF, 1840 KIL, 1841 ROS, 1842 LIM, 1842 ANT, 1842 TIP, 1843 TIP, 1843 WSM, 1843 LOU, 1844 LIM*, 1844 KIL, and 1844 ANT.
For Elizabeth McDonnell M ditto, I found 22 rcds. Only the asterisked yr/cnty above is a POTENTIAL match. Searching at the parish level, this wasn't a match. 1840 doesn't seem to be the right range. Suggest you try something earlier - like 1830 +/- 4 yrs.
For Elizabeth McDonnell B 1805-1811 somewhere in Ireland with the father's forename unknown, I found 5 rcds: 1806 Westmeath, 1806 Antrim, 2-1810 Armagh, and 1810 Limerick.
For James Dooley B 1805-1810 ditto, I found 6 rcds: 1805 Limerick, 1807 Kilkenny, 1808 Limerick, 1809 Kilkenny, and 1810 Kildare.
Will let you search the database for the remaining names.
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.