Can any Pokemon learn False Swipe, Mean Look, and a move to inflict paralysis or sleep?

Solution 1:

There are 2 Pokémon that can learn that combination of moves via TM and breeding.

Absol can get Mean Look as an Egg Move from Umbreon, can learn False Swipe from TM, and can learn Thunder Wave from a TM.

Gallade can learn Mean Look as an Egg Move from most ghosts, learns False Swipe naturally at level 45, and can opt for either Thunder Wave as a TM or Hypnosis as a level 50 Kirlia (this route would require you to use either the Move Tutor or a TM for False Swipe, but Sleep is better for catching).

Solution 2:

If you want to look up moveset combinations, check out Serebii's Moveset Calculator. For the moves you want, Absol, Gallade and Smeargle will work.

Personally, if you want something effective, I used to have a Smeargle with the following moveset:

• Spore (100% chance of sleep)
• Mean Look
• False Swipe

With the fourth slot being anything of your choice. I can't remember what I had. I think it was Odor Sleuth in case I needed to catch a Ghost-type.