The link I posted earlier is now dead; YouTube says the video has been "removed by the user."

However, I found this one, an actual video of an actual concert performance by the Irish Rovers. (as opposed to an audio track accompanying various still pictures, which is what you often see at YouTube) Click here!

The video is posted under the title "Irish Rovers-Old Rocking Chair" but when he introduces the song, he calls it GRANDMOTHER'S OLD ROCKING CHAIR. I've listened, and verified that it's the same song, with a few minor differences in wording, as the one recorded by Brian & Michael.

I haven't found any evidence that the Irish Rovers ever recorded the song.