Bowling greens in Oakdale, New Tredegar, Ynysddu, Senghenydd, Machen and Penyrheol could close under council plans to save £100,000.
The six could close over a two year period beginning in 2015.
The proposals were due to be considered at a recent meeting of Caerphilly County Borough Council’s Special Regeneration and Environment Scrutiny Committee but the meeting has now been postponed to July 30.
Ward councillors Margaret Sargent, Steve Skivens and Lindsay Whittle AM are opposing the closure of Penyrheol following representations from the local bowling club, which is due to celebrate its golden anniversary in 2016.
Cllr Sargent said: “Clubs like that of Penyrheol are what keep communities together. It is things on your doorstep that people value most and want to retain.
“Closure would be a devastating blow to the community and the council need to look at alternative ways of saving money. The club does a lot of work with young people in the community which would be lost if it was shut.”
Lindsay Whittle AM, who is also a ward councillor, said: “I remember Penyrheol Park being developed when I was a boy and I’m not prepared to stand by and see the council close it.
“The proposal to shut the bowling green defies logic. The club has a large membership and, importantly, the club holds coaching sessions for local youngsters, as well as new bowlers and has hosted classes from Cwm Ifor school.
“Bowls is very popular across Caerphilly county borough and in 2012 bowls players from across the globe came to Pontllanfraith for the World Indoor Bowls Council Championship.”
The Penyrheol club, established in 1966, is also involved in fundraising for charity and has raised £9,500 over five years for Velindre Hospital.
Aneurin Evans, Chairman of Penyrheol Bowling Club, said he understood the council had to save money but was hopeful the green could be saved.
A spokesman for Caerphilly County Borough Council said: “This is one of a number of savings proposals being put forward as the authority faces unprecedented financial challenges over the coming years. This particular proposal will be discussed by members of the council’s Regeneration and Environment Scrutiny Committee later this month. Those discussions will be fully considered at a future meeting of full council before any decisions are taken.”