For a start on print references, a quick look at a few old copies of the South Yorkshire Folk Diary shows the term in use in 1978 (ad for Wath On Dearne May Welcoming), so it was presumably well known at that time. Clubs that booked guests were more likely to describe non-guest nights as 'singers nights', though, and clubs that didn't tended to call themselves 'singers clubs' rather than 'singarounds'; that term seems to have been used more for one-off or occasional events.