Bicycle bearing grease!!!!
I've used that stuff in just about everything. I repacked a wheel bearing in a 1995 S10 and drove it without issues for another 100,000 miles. I've used it in motorcycle swing arms, head bearings, assemblies, etc. It just plain works. Oh, it totally rocks on bicycles too!
My logic is this: a bicycle wheel uses ball bearings (very small contact patch), so the contact pressures, and temperatures, are very high, especially when loaded. Considering I have never had any issues with my bicycles using that grease, I figured it would work well on other bearings.
Okay, all the chicanery aside, that swing-arm doesn't experience much motion. Just make sure you get a good petroleum or silicon grease in there, and keep it lubed. It really doesn't matter what you put in there as long as it is thick enough to stay in place.
Camelman