Just piping in to agree with Steve Gardham, and to add to Mudcat's collective knowledge on this song. The original line seems to have been "sing their merry lay" or "merrily sing their lay."

Steve's evidence was not entirely definitive, because it was based on Roy Palmer's transcription of a revival performance by Derek and Dorothy Elliott, not on a broadside or a source singer. The Elliotts' performance was apparently based on a recording of Kit Jones, a Yorkshire farmer, which I'd love to hear, just to confirm the word "lay." But until I do that, I still consider that text to be a product of professional folk-revival interpreters.

However, I've found an earlier text that is clearly a version of "Country Life," and that has "lay" rather than "laylum." It was published by Gavin Greig in his Folk-Song of the North-East column in the Buchan Observer in around 1911, with the title "The Country Life" (column number CLXIX, for those who want to check it out). He got it from F.R. Brown, an amateur song collector, but gives no other account of who the informant might be. He notes that it sounds to him like it comes from "the south," by which it's unclear if he means the south of Scotland or even further south. His version of the "little birds" verse goes:

I like to hear the little birds
Merrily sing their lay
Hurrah for a life in the country
And a romping in the new-mown hay

It's intriguing to me that this earliest text is located so far north in Scotland and that it has subsequently been collected only in Yorkshire. I wonder if it would be traceable to other Scottish sources?