just so long as they are not Babbitt.

Why? Babbitt has been a good bearing material for all sorts of things, from cart axles to engine crankshaft bearings. Even wooden bearings were used in a lot of machinery back in the last century and before.

I'd also be inclined to check that the greaseways are clear and not choked with old congealed grease first. Give the grease cups a good clean out too. A good quality NGLI No. 2 lithium based grease should do the trick. Most wheel bearing greases fall into that category.

These are as others indicate, called 'Stauffer Lubricators", and were very common before the invention of pressure grease-guns and nipples. They are just as effective, simply less compact.

I think you'll find you need fill both the cap and cup, on the first charging, unless the cup is of much smaller capacity than the cap. They are often of similar sizes, so filling only one part won't push much down the grease-way to the bearing.

My approach would be:

Clean out the lubricator and grease-drilling thoroughly.

Fill the lubricator fully as above, cup and cap.

Wind the cap down until grease just starts to appear from the bearing, while gently turning the machine over by hand to distribute it. (Obviously having put an initial smear of the same grease on the bearing, during assembly.)

Then refill the lubricator and as Brian says, give the journal a periodic half-turn dose.

If the bearing-housing is very thick-walled or the journal has big grease-grooves in its walls, those cavities can themselves absorb an appreciable portion of that initial lubricator-full.

Something like a wooden ice-lolly stick or a narrow semi-rigid plastic plant-label is effective as a grease spatula.

I would think modern greases would last a goodly time before a new squirt is needed, but that can only be determined by experience with the specific machine, and it is better to clean up exuded grease than renew a dried bearing.

The usual way or working with Stauffer greasers is, once the passages are clear, lubricant is reaching the bearings, to give the cap half or a complete turn every so often, say every operating hour or so, to ensure that the bearing is lubricated.

Initially, it may well be worth using a fairly thin grease, to ensure that it does reach, and leak out of, the bearings. Once you are happy with the lubrication, you can use a heavier grease if you so wish.

Howard