Would it be appropriate if our scouts build a course for an Eagle project?

Yes. However, it’s imperative that a professional designer be involved for the design phase so the course is not only suitable for those who will play it but also as safe as possible. A contact list of designers who can help find someone to help if they themselves aren’t able to help directly is available here. Typically, Eagle scouts have been doing something to improve an existing course versus building a course. Some of these improvements might be building several sets of steps to reduce erosion in places with grades, creating and installing tee signs with nice graphics, or building benches for each hole.