The Eels need to defeat Penrith away on Sunday and hope the Dragons beat Brisbane this Friday night at Suncorp Stadium or else their season is over.
But the odds of that happening nosedived further on Wednesday when Cooper withdrew from the Dragons' squad with a quadriceps injury he suffered at training on Tuesday.
Prop Ian Donnelly (hand) is also out of the team named on Tuesday.
The news came less than 24 hours after the club announced former Kangaroo centre Mark Gasnier (quadriceps) and winger Nathan Blacklock (knee) had also pulled out.
They join fellow big guns Trent Barrett, Jason Ryles, Lance Thompson and Brett Firman on the sideline.
Dragons coach Nathan Brown has been forced to make wholesale changes to his squad, including moving Test five-eighth Shaun Timmins into the second-row, shifting Ben Hornby from fullback to pivot and drafting in No.1 Reece Simmonds.
Back-rower Robbie Simpson has been added to the bench and will become the joint venture club's 12th NRL debutant this season.
St George Illawarra's new squad is: Reece Simmonds, Hassan Saleh, John Wilshere, Chris Nero, Ben Creagh, Ben Hornby, Mathew Head, Luke Bailey, Mark Riddell, Chris Leikvoll, Brent Kite, Shaun Timmins, Dean Young. Interchange: Ashton Sims, Craig Stapleton, John Cross, Robbie Simpson.