If this photo is taken at an actual match, and the players are correctly named, then there are 4 strong candidates - partly because the opposition was Rangers or Celtic and it was the start of the season. Johnny MacKenzie was transferred to Dumbarton in mid-August 1960 so it can't be any later. Curran played regularly for the reserves the previous season but can't find any obvious match with the players named.
13/8/60 Rangers H Reserve League Cup 3-6 is the closest match except no Wardlaw.
Curran, Muir, Thomson, Brown, Staite, Cunningham, MacKenzie, Wilson, Fletcher, Hastings (?), Waugh.
16/8/60 Celtic A Reserve League Cup 0-2.
No team information however.
23/8/60 Rangers H Reserve League 3-2.
Cunningham (2) and Wilson scored but no other team info.
26/8/1960 Rangers A Reserve League Cup 1-9 (ouch!) is another possibility but Mackenzie played the following day against Rangers at Ibrox (his final game for the club) so, while possible, it's unlikely.