how do you grease a coaster brake?

I've got a long way to go myself, but I know what my experience has been. If it's squeeling then youre hearing dry metal to metal. There are tutorials on coaster hubs and they recommend a light coat of bearing grease on the pads that grab the hub. I went crazy with the grease and put about 10 times more than recommended. I tried to put so much in that when assembled it would ooze out and it did. The brake works fine. The pads have grooves for channeling the grease away.

I'm not sure but you might be able to force grease into the hub by removing the dust cap and first bearing. Just keep smearing grease into the seat until it comes out the other side.

Here's a link to Sheldon Brown's (RIP) coaster brake section. He has links that teach you how to do it.
Bicycle Coaster Brakes
Especially this link from him:
Park Tool Website
Here's another link from his site as well:
Overhauling a Coaster Brake Bike

Have fun with it!

if you're gonna do it, might as well do it right. the brake shoes in a shimano hub will last at least a hundred years (seriously) without grease. the bearings won't last a week.

take the time to pull it all apart and grease all the bearings. there's three bearing races in there, y'know.

if the shoes are squeeking from lack of grease, that means the bearings don't have much in them either.

look at it this way. if you do a halfway job and just try to grease the shoes up, after the bearings freeze up, it won't squeek at all. and the brake will work so good the wheel won't roll at all.

2 Fold when I rebuild my CB hubs...

...Bel Ray Salt Water proof Moto grease on my bearings and Klotz R50 Moto 2 stroke oil in the hub, the salt water proof grease is good enough on my boat trailer when I submerge the wheel bearings every time I unload/load the boat, and it holds the Klotz R50 in the CB hub. It runs and lubricates Motos internal combustion engine parts under very high temps that a CB hub will never see. Klotz R50 contains Castor bean oil. ‘Bean Oil’ as it is often referred to, very unique characteristics The good is that it is an excellent lubricant. It seeks out hot spots in the engine and clings to those hot surfaces much better than petroleum type oils. I love the unmistakable ‘sweet’ smell.

I think its just wearing in. I recently got a Shimano coaster brake as well, and serviced it myself, and greased everything up liberally as I always do. Was out for a late night cruise last night, and decided it was a good time to test the new brake (I have a front drum as well, just wanted to see what the shimano brake could do). I felt the brake grab as soon as I pushed back on the pedal, but heard a terrible squeal. With the amount of hi-temp grease I applied, there is no way that anything in that hub was dry enough to make it squeal like that. And its all brand new components, so I figure it must be a break in type of thing. I don't use my back brakes very often, so it doesn't concern me too much.

I agree with you bbb, the brake shoes will arc themselves to the inside of the drum just like the brake shoes do on all other sorts of drum brakes.