The ban effectively rules the pair out for the rest of the season with their final game of the campaign in 10 days time.
Fourth-from-bottom Reading, who are just one point ahead of 18th-placed Birmingham, face Spurs at home before a trip to Derby for a match which could decide their Premier League future.
Coppell was reported to be furious when Sonko and Fae said they would not play against Tottenham reserves at Aldershot.
Club captain Graeme Murty and John Oster were among the first-team squad members who did turn up for the 2-2 draw.
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