For James Dwyer B 1867 +/- 5 yrs, Co. Tipperary, with a father forenamed Jer(emiah), I found 0 rcds. I get the same result searching 25 of Ireland's 32 counties.
For Jer(emiah) Dwyer M 1863 +/- 4 yrs, somewhere in Ireland, I found 3 rcds: 1860 Tipperary (Powerstown RC), 1865Tipperary (Bansha CP), and 1866 Limerick (Ballylanders RC).
For Bri(dget) Mulcahy M ditto, in the same counties and parishes found for Jeremiah, I found 0 matching records.
For Marg(aret) Todd M 1869 +/- 4 yrs, somewhere in Ireland, I found 13 rcds - too many to easily research and summarize here.
For Pat(rick) Dwyer M ditto, in the same counties found for Margaret, I found 35 rcds - again too many. Will leave it to you to delve deeper into the database using the FREE search features to see if there is a match for the same yr/cnty/parish.
For Jer(emiah) Dwyer B 1877 +/- 4 yrs, Co. Tipperary, with a father forenamed Pat(rick), I found 3 rcds: 1878 Cappagh CP, 1878 Kilcommon RC, and 1881 Kilpatrick CP.