Probably a bit of a logistical nightmare, but if a few days before a match the club definitely know they are not going to sell-out, why don't they contact some local schools and give them free tickets?
Would ensure a full-house and they would pick up a few converts along the way (take a ten-year old kid to the Amex to see his first football match, and he could end up a life-long fan...). The club would also make a bit of extra money from merchandise sales.
During term time this would be a good idea however I feel a voice mail coming when they ring the Schools at the present....