Cooper, 31, was playing for Culcheth Eagles at Runcorn ARLFC and had been substituted when he began to feel unwell at the start of the second half.
An ambulance was called but they were unable to save the father of three.
Rugby Football League officials are supporting the family of Cooper and a donation page has raised over £8,000.
Culcheth Eagles junior sides played as normal yesterday, with all matches preceded by a minute's applause.
No decision has been made about whether the planned open-age league match at Cadishead Rhinos on Saturday will go ahead as planned.
"It is awful," said Culcheth Rangers' vice-chairman Jo Eland. "Adam was just a young lad going out to play the game he loved."
Cooper was a longstanding member of the club and returned from Leigh East to play with them when they re-established their open-age team in 2010.
A minute's silence will be held before every rugby league game this weekend in memory of amateur player Adam Cooper who died during a match on Saturday.