I searched 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. Portions of Co. Galway rcds are in the database.
For Robert Rutherford B 1781 +/- 4 yrs, I found 1 B rcd in 1785, Co. Down.
For Robert Rutherford M 1802 ditto, the earliest M rcd is for 1813 in Sligo, the next is 1820 in Down.
For Mary Sommerville M ????, the earlies M rcd is for 1827 in Antrim.
For Mary Sommerville B 1785 +/- 4 yrs, the earliest M rcd is for 1829. It is unlikely to be for your ancestor.
For Robert Rutherford with a father named Robert, the earliest B rcd is for 1853. Again, this doesn't fit your timeline.
It looks like rcds for the B & M events weren't rcd'd or didn't survive.
Google the Foundation's name to lead you to this database. Pls post your search results to this genforum msg.