Not something I've gone looking at, but my first recollection of teams having two jerseys in same year was Wests & Manly in 1975, but that was really confined to just the pre season jersey differing from the premiership - Manly, and maybe Wests, played in white jerseys. Manly made the change to white permanent in 1976, but stuck to one jersey.
It seems that shorts, socks, and some differentiation in the jersey by the second colour (white being the first colour), was sufficient to keep at bay any complaint that team kits clashed.
I may be wrong, but I think Wests thru late 1970s were first to have two jerseys in same season, but the concept of every club having an "away" jersey is much more recent.