I think:
Bulbasaur - Seed Bomb (Isn't that common, might stop Bulbasaur being called repetetive.)
Squirtle - Aqua Tail (It's all I can think of, really.)
Charizard - Air Slash/Shadow Claw (Something that keeps him a bit different.)
Kingler - Flail/Tide (Now that I've seen Sudowoodo's Flail, I love it. And Tide just sounds amazing.)
Tauros - Reminiscent Headbutt (Just because :/)
Muk - Dust Shoot/Mud Bomb (Sound okay on him.)
Heracross - Bug Upheaval (His horn makes this sound amazing XD)
Bayleef - Aromatherepy/Light Screen/Nature Blessing (Nature Blessing needs to be showcased well, I think.)
Totadile - Ice Fang (Maybe?)
Cyndaquil - Flame Wheel (With an evolution of course. I want him to be amazing.)
Noctowl - Extrasensory (Needs a new Psychic attack.)
Donphan - Stone Edge (Because I can't think of anything else.)
Swellow - Beak Peck/Endeavor (Endeavor sounds good, but I'd like Beak Peck too.)
Sceptile - Detct/Scissor Cross (Both are good.)
Corphish - Blade Test?
Torkoal - Smoke Erupt, definately.
Glalie - Not sure at all :/
I don't think In-Fight or Brave Bird will be learned, since they're perfect moves that will make Mukkuhawk unique. Especially Brave Bird, since (apart from Blaziken) is a Mukku-line exclusive move (learned naturally).
Iota