Killjoys in Bristol want to introduce the fines after receiving 3,000 complaints about anti-social behaviour in open spaces over two years, although only 92 were about nuisance in parks.
According to local news, officials have drawn up a list of 39 proposed new rules which also ban barbecues, skateboarding and windbreaks.
And they want to give police, community officers and dog wardens the power to hand out £500 fines.
The report says: "No person shall without reasonable excuse climb any wall or fence, or any tree, or any barrier, railing, post or other structure.
"No person shall play ball games outside a designated area for playing ball games in such a manner as to cause danger or give reasonable grounds for annoyance to any other person."
But angry councillors blocked a vote on the move.
Councillor Dr Mark Wright said: "This is a massive over-reaction to issues that are better managed by education and common sense.
"The vast majority of city-centre residents have no garden. For them, public parks are the only open space they have access to."
Bristol's mayor George Ferguson stepped in on Tuesday to stop the vote and send the plans to a scrutiny group.
An official said the rules would only be enforced in parks where there had been complaints and as a last resort.
He said: "The powers were not about banning people from enjoying activity."