Complete episode list
I found the complete episode list for Tanoshii Moomin Ikka and its sequel Tanoshii Moomin Ikka Boken Nikki.
The original 78 episodes were dubbed in English, but not the 26 episodes of the sequel. Your ownly way to watch these is to buy the DVDs from YesAsia. But they are Japanese with no subs. Which isn't much good if you don't understand Japanese.
EPISODES
Season 1: 'Tanoshii Muumun Ikka' ('The Delightful Moomin Family')
TX: 10.10.1991 - 26.03.1992 (Tv Tokyo):
Episode 1: ‘Spring in Moominvalley’
Episode 2: ‘Magic Hat’
Episode 3: ‘Shipwreck Found on the Beach’
Episode 4: ‘Welcome to Ghost Island’
Episode 5: ‘Nyoronyoro's Secret’
Episode 6: ‘Small, Small Visitor’
Episode 7: ‘What's Inside the Suitcase’
Episode 8: ‘Magic Trick of the Flying Demon’
Episode 9: ‘Invisible Friend’
Episode 10: ‘Ninny Gets Her Smile Back’
Episode 11: ‘Snork Flies in the Sky’
Episode 12: ‘Moomin Fights a Pirate’
Episode 13: ‘Last Dragon on the Earth’
Episode 14: ‘The Nextdoor Neighbor is a PTA Mom’
Episode 15: ‘Floren Gets Amnesia’
Episode 16: ‘A Martian in Moominvalley!’
Episode 17: ‘Moominpappa Runs Away’
Episode 18: ‘Magic Seed from the Sea’
Episode 19: ‘Moominvalley's Jungle’
Episode 20: ‘Moomin Saves the Tigers’
Episode 21: ‘Snufkin Departs on a Journey’
Episode 22: ‘Moomin and Mee's Big Adventure’
Episode 23: ‘Moominvalley's Winter Inhabitants’
Episode 24: ‘Snufkin Doesn't Come Back’
Episode 25: ‘On Papa's Dream’
Episode 26: ‘Days When the Lighthouse Shines a Light’
Episode 27: ‘Rich Mrs. Jane’
Episode 28: ‘Floating Haunted House’
Episode 29: ‘Separated Family’
Episode 30: ‘Reunited’
Episode 31: ‘Snork's Flying Ship’
Episode 32: ‘Rare Goldfish’
Episode 33: ‘Make a Wish to the Lamp’
Episode 34: ‘Mee Gets on a Kite’
Episode 35: ‘The Witch Comes Home’
Episode 36: ‘What's Christmas?’
Episode 37: ‘Festival of the Winter Creatures’
Episode 38: ‘Sleep Magic’
Episode 39: ‘Mysterious Sound in the Middle of the Night’
Episode 40: ‘Secret of Fireworks’
Episode 41: ‘Strange Incident in Moominvalley’
Episode 42: ‘Magic Broom’
Episode 43: ‘Heroine of the Circus’
Episode 44: ‘Wonderful Birthday’
Episode 45: ‘The House Built by Moomin’
Episode 46: ‘Papa's Rich?’
Episode 47: ‘A Hot Spring Appears!’
Episode 48: ‘Moomin Rides on a Bubble’
Episode 49: ‘Mama's Secret’
Episode 50: ‘Voice from Inside the Dead Tree’
Episode 51: ‘Floren's Psychic Powers’
Episode 52: ‘Water Fairy’
Episode 53: ‘Treasure Hunt Uproar’
Episode 54: ‘Gift for Mimura’
Episode 55: ‘Sad Papa’
Episode 56: ‘Mama Departs on a Journey’
Episode 57: ‘Floren Raises a Child’
Episode 58: ‘Contest in Moominvalley’
Episode 59: ‘Papa's Memorie’
Episode 60: ‘Mee's Prank’
Episode 61: ‘Moomin's a Genius Fortuneteller’
Episode 62: ‘Magic Word’
Episode 63: ‘Adventure of the Ship Orchestra’
Episode 64: ‘The Day of Leaving the Nest’
Episode 65: ‘Moomin's Secret’
Episode 66: ‘Vampire of Moominvalley’
Episode 67: ‘Papa's Important Seat is Broken’
Episode 68: ‘Fateful Meeting with Mama’
Episode 69: ‘Crisis with the Immortal Bird’
Episode 70: ‘Making up at the Fish Party’
Episode 71: ‘Identity of the Glowing Mushroom’
Episode 72: ‘Friendship of Moomin and the Dolphin’
Episode 73: ‘Moomin's Explorer Team’
Episode 74: ‘Singing Flower Present’
Episode 75: ‘Moomin's Lovely Dream’
Episode 76: ‘Broken House’
Episode 77: ‘Finished! Flying Ship’
Episode 78: ‘Moomin into the Open Skies’
Season 2: 'Tanoshii Muumin Ikka Boken Nikki' ('The Delightful Moomin Family: Adventure Diary')
TX: 12.04.90 - 03.10.91 (Tv Tokyo):
Episode 79: ‘The Ring on a Finger’
Episode 80: ‘The Girl With Birds’
Episode 81: ‘A Wind of Freedom’
Episode 82: ‘Mr Caramel’
Episode 83: ‘A Real Gold Mine’
Episode 84: ‘Sand Sculptures’
Episode 85: ‘The Beach’
Episode 86: ‘A Bothersome Nephew’
Episode 87: ‘The Time Travel Machine’
Episode 88: ‘The Circle of Secrets’
Episode 89: ‘The Dragon’
Episode 90: ‘The Desert’
Episode 91: ‘Queen Cleothystra’
Episode 92: ‘The Treasure Map’
Episode 93: ‘A Sniff at Everything’
Episode 94: ‘Funny Disguises’
Episode 95: ‘Moomin in Cowboy Country’
Episode 96: ‘Moominson Crusoe’
Episode 97: ‘Hidden love of Pretty Mee’
Episode 98: ‘Tears of the Dragon’
Episode 99: ‘Chouca Lisa’
Episode 100: ‘The Night of the Red Moon’
Episode 101: ‘Return to childhood’
Episode 102: ‘The Birthday Surprise’
Episode 103: ‘The Moomins and the Fake Yeti’
Episode 104: ‘The Starry Voyage’