Steven+Rose: Fairy/Grass
Garnet: Fighting/Psychic (with Electric moves included in moveset)
Pearl: Fairy/Flying or Fighting/Flying (Steel type/moves involving blades and cutting in moveset to reflect her swordfighting)
Amethyst: Fighting/Poison (or maybe pure Fighting with Poison moves in her moveset)
Peridot: Steel/Psychic
Lapis: Water/Flying
Jasper: Fighting
Ruby: Fire/Fighting
Sapphire: Ice/Psychic
Bonus:
Connie: Normal (maybe Fighting or Steel as a secondary)
Stevonnie: Normal/Fairy
Opal: Fighting/Flying or Fairy/Flying (depending on which type Pearl has
Sugilite: Fighting/Poison
Sardonyx: Psychic/Fairy or Psychic/Flying
Alexandrite: Fighting (huge coverage tho)
Smoky Quartz: Fairy/Fighting
Malachite: Water/Fighting (with Flying coverage)
Yellow Diamond: Electric/Psychic (we haven't seen much of her but I theorize she'll have electric powers)
Greg: Normal
Onion: ???
Every Gem character has Rock type coverage.