Harrogate Borough Council’s insurers agreed to pay just under £48,000 to replace the fort but the policy’s excess amounted to £5,000.
"This is the target the friends have set themselves so they can help the council make sure that the replacement is of equal value," said group chair Jane Blayney.
Her organisation is seeking donations from individuals, local businesses and community groups.
"Like the council we want to act quickly to fully reinstate this much-loved playground," she said.
Councillor Caroline Bayliss said: "The fort was the centrepiece of the play area and we want the replacement to have the same wow factor."