Small go board history
A Japanese pro 9-dan, Tomoyasu MIMURA (born 1969) writes in his blog entry (3 Feb 2014), ''I had never seen, or heard of 9x9 board in my childhood'' and ''In 1987 started the TV show 'Mini-Go One Game Match (ミニ碁一番勝負)'.... Professionals had begun to pay attention to the unexpected depth of 9x9 board game some time before''. 
Therefore, around 1985 would be a good guess.