A run of two wins in 17 games has left the Potters out of the FA Cup and looking over their shoulders at the fight for Premier League survival.
Tony Pulis' side retain a nine-point cushion on the bottom three, and the manager who brought Stoke back into the top division after a 23-year absence still has the support of his chairman, if not some of the club's fans.
Now Coates has called on supporters to prove their loyalty by renewing their season tickets.
He told The Sentinel: "I think we are a bit behind (on sales), but every year we are trying to improve. We have the best squad since promotion and we want our supporters to stay with us.
"We all want the club to progress, and to do that we need our supporters. They are vital on the day and I would also like to think they will stay as season ticket-holders.
"I am not saying don't moan and groan, and I am not criticising supporters for that. But we need our supporters."
On Pulis, he said: "Tony has done remarkably well for this football club, but every club in the Premier League has a lean spell at some point.
"I understand we are having a bad time, and if you don't get results and don't play well then managers get criticised, but there has to be some balance."