Time is running out for organisers to reach the Â£15,000 target to install the ride in Sandall Park.
Organisers, the Friends of Sandall Park, have a fortnight to bring in more than Â£5,000 of pledges - with more than Â£9,000 already donated so far.
Spokesman Sandra Crabtree said: "So many people have got behind this project, which is fantastic.
"Please pass this message on to at least two of your friends, business colleagues or relatives, and ask them to do the same.
"We are so close to reaching our target, and also so close to the closing date. It would be fantastic if local businesses could contribute and increase our chances of success."
She added: "The level of support has been tremendous, those people deserve to see their pledges turned into reality. Let's turn this project into a real success story for Sandall Park and for Doncaster."
The appeal was started so the park can extend its range of play equipment.
The Wheatley park already has an inclusive 'nest swing' installed for less able children to be able to play with their siblings and friends.
Added Sandra: "This invites people from the community, as well as businesses to pledge money towards the funds required."
"No money will be taken from accounts unless the full amount is reached.
To make a pledge, log on to https://www.spacehive.com/i-can-play-too#/idea