Okay, here is the deal guys and non-guys, I'm not really a big fan of the current natural wonder system.
The wonders are currently split into three groups. The first group just provide you with a tile with 9 yields, which is definitely fine (assuming the wonder in question is not Cerro de Potosi or El Dorado). The second group are the ones that provide you with +1 happiness for being inside your territory and then provide you with a 6 yield tile, there is a gigantic difference between a 6 yield tile and a 9 yield tile, and getting +1 happiness means pretty much nothing with how the happiness-system currently operates.
The third group, the one I find the most interesting are the odd ones out, they are a group simply because they don't act like the other wonders at all. It consists of two wonders, the first one being the Barrier Reef, it starts out as two 8 yield tiles that grow when you add lighthouse, harbor, seaport to the city controlling them. Despite being ocean-based and therefore more often than not spawning just outside of reach for any city, the wonder to me remain interesting because it occupies two tiles.
The second wonder in the group is the Mt. Kilimanjaro, a 9 yield (and actually 9 good yields) wonder that uniquely provides visiting units a unique promotion that gives them the ability to move faster in hilly terrain. The wonder is interesting because it is comprised of two different parts, the active part where you work the wonder and gain 9 yields and the passive part where your military units have a slight advantage over hostile military units.
My main idea here is to apply the Mt. Kilimanjaro concept to all the natural wonders in the game, letting them have one active part and one passive part. In my opinion a natural wonder should be something worth fighting for, something worth forward-settling for, something worth using a great general for or attacking a city-state for, and I just don't see the current natural wonders as holding that value, even for Polynesia, at best you're receiving a slightly buffed up great tile improvement and at worst you're getting +1 happiness and a tile that you wish you could farm for adjacency-bonuses.
The Active Part:
I think 8 yields sound like a good plan, an even number also makes the Polynesian UA happy.
The Passive Part:
This is the hard part. First of all I don't know if this is at all possible, but I would love to see these passive abilities being global, something along the lines of "As long as this wonder is within your territory, all units produced starts with the Altitude training" instead of all units moving next to the tile receive the promotion. Mostly because of the annoyance of actually having to send all your units over to the wonder, I also don't really see the AI handling the wonder very well, so something like this would probably help them.
As for the passive part itself, it doesn't necessarily have to be promotions at all, it could range from something like a global +5% gold(or any other yield) or a bonus when recruiting units. The effects could range between the power of a bottom-tier wonder or maybe half the power of a monopoly-bonus. Some wonders could provide promotions like Mt. Kilimanjaro, maybe bring back a lesser version of the old fountain of youth promotion (like +5 healing per turn instead of double healing).
The effect doesn't necessarily need to be amazing, the main thing is that they make natural wonders feel cool and interesting, and makes them worth getting into a conflict with your neighbor over.
So, thoughts?