That's not what "Normal" means. Normal, in the context of Pokemon, basically means a basic, non-elemental type.
So an opposite of Normal would be...literally every other type.
Yup. And honestly, what would be the opposite of normal in terms of gameplay? Weak to practically every type, but super effective against practically every type? Resistant to practically every type, but weak against practically every type? In the case of the former (weak defense, effective offense), that would be ridiculously OP. Keep in mind that in most RPGs, perks/items that boost your damage by a considerable amount (here by a factor of 2) generally lower your health or your resistances by a greater factor (3 or 4 from what I've seen). That would make no sense to introduce such a type.
Personnally, I really don't see the need for a new type. I feel like most types proposed are sort of covered by other existing types. Some types I've seen proposed :
-> Light : Electric, fire. However, if there is one type that could make sense to add, though, it's that one, from a less realistic and more fantasy point of view. It appears in a lot of RPGs that have elements like fire or electricity as the "pure" element, which we dont really have in Pokémon - Fairy maybe if we want to stretch things up.
-> Cosmic/Alien/Celestial : Psychic, rock, steel. I understand a lot of Pokemon could get that type, with probably 75% of them already being psychic type without counting the UBs.
-> Sound : Flying, normal. And honestly, that doesn't even make sense as a type. As said previously, it's more of an attribute.
-> Air : Flying. Nothing more to say. Flying is the equivalent from the popular air element in most other RPGs. It would be extremely redundant.
-> Crystal : Rock. Crystals are rocks. Maybe ice for the "color" aspect.
-> Plasma : Electric. That's literally what plasma is; ions.
-> Shadow : Dark, ghost. Keep that to Pokemon XD.
So yeah, Light is probably the only one that I'd be on board with. As far as potential Pokémon that could receive it, I could see the following : Lanturn, Ampharos, Volbeat, Illumise, Solgaleo, Lunala, Necrozma, Lumineon, Xurkitree.
And for the type chart, something like that :