Check your project plan guide. You are responsible for the funding, and your fund raising can count toward volunteer hours to get the project done.
You need to know the costs. (I assume you have approvals from the Park, and from your district advancement committee, yes?) Get a basic description of the project, and put together a PowerPoint or KeyNote production describing the project and benefits. Note your budget, and take the show on the road.
Who is the charter organization for your troop? Check with auxiliary groups of that organization and ask for contributions, with effusive thanks to the people for sponsoring your troops as you go (get a stack of fancy thank-you notes, and write them early and often -- this will increase contributions). For example, our son's church's men's organization was happy to learn about the project, and without our asking pledged a few hundred dollars to get it done.
Consult with other civic organizations in town, give them the slide show, and ask for help.
National chain hardware/lumber stores often contribute materials for projects -- Wal-Mart managers have a budget for such things. Check with Lowe's and Home Depot.
Is there a local support group for the Park? A local chapter of the National Parks and Conservation Association? Ask to meet with them and ask for money. How about the Georgia Historical Society? Have you approached your local chapter of the Audubon Society? Who else would have an interest in seeing the project be successful?
Perhaps there is a local chapter that stages battle reenactments. They might be particularly interested in such a project, and you should write to the group and ask for support.
Write to every relative you have. Ask for small donations. Some aunt you didn't know was rich will give $100. Some other aunt who isn't rich but loves you will give $150, and she'll frame your thank-you note.
Scouts in our troop have sold hotdogs and sodas before troop meetings, or at local soccer or baseball matches where there are not concessions, usually.
Be sure you keep exquisite records on who gave how much money, and how the money was spent. That should be a part of your final Eagle packet to the district advancement committee and National Council.
By the way, you should include in your budget money for a small plaque to go sowewhere to list and thank the donors. It might be mounted on the fence, on a stone placed by the fence, or in the Park's Headquarters.
Boy Scout Handbook
Eagle Scout Application