My five suggestions are:

Gems:
I don't care what you say, Shane, but I consider Gems to be separate from Earth.
Besides, gems are rare, so why not?

Fairy:
I consider Fairy to be different from Star. After all, there could be Dark Fairies, or Thunder Fairies, or even Data Fairies.
(Who knows what goes on in the Endanian world.)

Psychic:
I don't think Psychic is "magic". Therefore, I suggest this as well.

Moe:
Eh... heh heh. Sorry.
I just think this ought to be an element
In my opinion, this would be the most embarrassing way to defeat a monster

Chemical:
This, I consider, would work well regarding the chemical elements (like chlorine, oxygen, gold, hydrogen, plutonium, arsenic, lawrencium, mendelevium, iodine and so on), and all things related to this element would deal damage of two elements (such as Chemical damage and Poison damage if it's caused by chlorine, or Chemical damage and Metal damage if it's caused by gold). This element would be the most difficult to implement, however, it's just a suggestion.



If you choose to use those elements, you can do with them as you like; abilities, weaknesses, strengths, you can choose.