I agree with maplebones that the bearing may not be at the end of its useful life.

I had a 240 with the same symptoms. The original carrier bearing's plastic "seal" was fairly easy to dislodge enough to get a spray can straw behind. Things had to be moved to get at it but it remained in place.

I used a product called LPS3. It is sold in 11oz aerosol containers. It sprays as an oil but the contained vehicle evaporates and leaves behind a light grease. I loaded the area behind the seal as much as possible. This not only cured the immediate problem but it remained quiet for years after having two additional owners until I was able to buy it back. I then sold it to a friend who had it for several years before he passed it on to a new owner. At that point it still had the original carrier bearing.
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Any twenty minute job is just a broken bolt away from a three day ordeal

Hi,

I think it unlikely very much grease will penetrate the seal on the center bearing if just sprayed on.

A better option that will give you immediate relief is to get a hypodermic needle for your grease gun and shoot some grease in between the outer race and the seal. Don't try to puncture the seal as I once did. You might break the needle.

The whining does not necessarily mean a failed bearing. Just one crying out for grease. It's a rugged unit operating on a small load. I've pulled 3 whiners on 240's I've restored and all were put back in service after pulling the seals, cleaning out the caked grease, and repacking. A short bath in boiling water will make seal removal very easy.

To inspect the bearing look for lateral movement between the inner and outer race, and signs of scoring or overheating. Before repacking, apply some oil to the clean bearing and hold it with the fingers of your left hand inside the inner race. Spin with your right hand. If it runs smoothly there's no reason to replace it in my opinion. One of the cars with a repacked bearing has now over 75k with no issue.

Peter