Correct me if I'm off-track, but teleconverters can be best taken advantage of with a large aperture lens, such as a 2.8 or larger aperture. The larger aperture enables better focusing sharper images due to the TC's inherent stop down effect. So, technically, you may not need an AF-S lens for best quality, like getting a non AF-S 80-200 2.8 for example, but of course you will decrease AF performance.
Not sure if anyone mentioned this in their posts, as I just scanned them briefly.
Most are used with f/4 or faster lenses. Plus like Matt said, Nikon has so many lens technologies still in use they have many different Tcons for them all. The ones I listed were for AFS lenses only. The others are for AIS (manual focus.) The sharper images has nothing to do with the f-stop, it's just that the f/2.8 lenses have much better optics to boot is what generally makes them a better choice to not loose detail when using a Tcon. The f/2.8 means they don't take as much of a AF sensitivity hit because the lens has more to sacrfice than an f/4 for example.
The specific lens you mentioned - AF-D 80-200 f/2.8 does not have a Nikon brand AF Tcon for it. The only Tcon they still make that will work won't allow the lens to AF. You will notice that I did not include the likes of the 70-300 and the 80-400 VR in my list, that's for the same reason.
There are not only 3rd party Tcons, but extention tubes that you may want to look at. Extension tubes give your lens a boost and allow them to focus more shallow (closer) whithout loosing any optical quality because there is no glass. The Kenko ones come to mind for Nikon.
OT - Methinks an updated 80-400 VR is due from Nikon one with AFS at the least giving it Tcon compatablilty while maintaining AF.