That would actually be quite interesting. So, after doing a little research, I think an hypothetical Fire-type "Pele Pokémon" should form a legendary duo with an hypothetical Ice-type "Poliahu Pokémon", since their counterparts are rivals in myths.
Anyway, from what I have found, there is actually a quartet of main deities in Hawaiian culture, which are:
- Kane, father of living creatures and the most important deity;
- Ku, god of war;
- Lono, god of agriculture and connected to rainfalls, peace and music;
- Kanaloa, god of the underworld and ruler of the ocean, is a close companion of Kane.
If these were to become Pokémon, I suppose they could have these types:
- Kane Pokémon: Ground / Normal / Dragon;
- Ku Pokémon: Fire / Steel / Dark (could have Final Gambit as an attack due to its counterpart getting many sacrifices);
- Lono: Grass / Ground (could have moves like Grass Whistle and Rain Dance);
- Kanaloa: Ghost / Water / Dark.
However, the Hawaiian culture is so full of deities that there shouldn't be any trouble finding some material for some legendaries. Among the most important ones there are:
- Pele (as previously mentioned by Vader_the_White), goddess of volcanoes which controls fire, lightning and wind. Potential Fire-, Electric- or Flying-type.
- Poliahu, goddess of snow and rival of Pele. Potential Ice-type.
- Hina, goddess of Moon. Potential Dark- or Fairy-type. Only issue is that it may clash with Lunala.
- Laka, goddess of hula. Potential Normal- or Psychic-type. Could learn many dance moves, like Petal Dance or Teeter Dance.
- Kuula, god of fishermen. Potential Water-type. Could have Suction Cups as its Ability.
- Papa, fertility goddess and Earth mother. Potential Ground-type.
If you would like to find more useful info,
this site illustrates many things about Hawaiian myths and legends.