Perhaps the most successful nonprofit conservancy managing a major park is the Central Park Conservancy, which is why we refer to it frequently.
Their history, posted on their website is illustrative;
"Over the past twenty years, the history of Central Park has been greatly affected by the history of the Central Park Conservancy, the private, not-for-profit organization that manages Central Park under a contract with the City of New York/Department of Parks and Recreation.
Perhaps the single most important ingredient in the modern restoration of Central Park is the successful public/private partnership between the City of New York/Department of Parks and Recreation and the Central Park Conservancy."
To read more go to http://www.centralparknyc.org/thenandnow