One way to make it quieter is to put a bit of grease under the keycap -- that softens the sound that the spring makes when it buckles. However after a while the grease can leak down into the keyboard membrane.
Another method is to put a piece of dental floss down inside each spring. Supposedly that reduces the sound quite a bit.
It's hard, because the Model M relies on a steel spring buckling, which is inherently noisy. You can dampen some other sounds (like the keycap hitting the key's fixture, either with grease, or permanently with rubber rings), but with how little space there is in a key, it's hard to silence that particular sound.
IBM themselves went with regular rubber domes for their "quiet touch" Model M variants, which are unpopular due to not being mechnical.
Another method is to put a piece of dental floss down inside each spring. Supposedly that reduces the sound quite a bit.