I searched the IFHF's ROOTSIRELAND.IE database. It has abt 4.5M marriage record and covers MOST Irish counties.
For a Col(man) Greene and Bri(dget) Burke marriage, I found 2 records in 1878, Co. Galway. These may be duplicates of the same event and MAY or MAYN't be for your ancestors. Will leave it to you to google the database register (free), and decide which, if either, is for your ancestors.