Is there a Pokémon that can solo the Elite Four without any restoring items?

These are the Elite Four trainers that you have to defeat:

• Malva, Fire-type
• Wikstrom, Steel-type
• Drasna, Dragon-type
• Siebold, Water-type
• Diantha, mixed team

You need a Pokemon that can learn a Ground move for Steel and Fire types, an Electric/Grass move for Water type and Dragon/Ice move for Dragon type.
For the last slot you can choose a Fire move (taking advantage from STAB) or a Rock move to have more coverage.

One is Charizard, and he has access to 2 megaevolutions. I suggest the Y versione due to Drought ability (lets you use Solarbeam without the charging turn and can increase Fire damage).

This is the set for Mega-CharizardY:

• Earthquake
• Solarbeam
• Dragon Claw / Dragonpulse (eggmove)
• Flamethrower / Heat Wave
• [Rock Slide / Ancient Power]

Of course you need a well trained Pokemon to do that, at least level 80 I suppose, because you need to oneshot most of them if you don't want to use healing items.

Palkia seems to be one of the best Pokemon to beat the elite 4 alone. It has got some really good attack stats (120 physical and 150 special) and isn't really slow (100 base stat). I recommend to maximize Special attack and speed with this move set :

• Spatial Rend would destroy Drasna team (max PP : 8 attacks moves would be sufficient)
• Earthquake or Earthpower, but I would recommend Earthquake in order to be able to make some damage on special defensive tank (like the Diantha M-Gardevoir); this attack would destroy Malva and Wikstrom, but not all due to double Fly type / Levitate
• Thunderbolt for Siebold's team and any Flying types (you can use Thunder, but only 70% accuracy could lead to missing an attack)
• Surf is a pretty good Water move that would finish Malva's team and Siebold's Water/Ground type.

Lustrous Orb is Palkia's dedicated item, but you can give him Leftovers to recover a few HP each turn against each Pokemon that you won't be able to OHKO

Let me introduce you to "Funbro" (Warning: this strategy will lose you any friends you have and requires a ton of patience)

1. Acquire Slowbro
2. Give him a Leppa Berry
3. Teach him Recycle, Slack Off, Block, and Heal Pulse (this last move is optional for you)

You now have a permanent stall Pokemon. For your specific situation, you could either just not use Heal Pulse or have him learn any other move. This is how your battles will typically go:

1. Use Block to prevent enemies from switching out or escaping.
2. If your Leppa Berry has been consumed, use Recycle.
3. If you don't think you can survive the next attack (or if you just feel like it), use Slack Off
4. Optionally, use Heal Pulse to keep your opponent from fainting.

Now, you can either stall the enemy Pokemon until they Struggle themselves to death or you could use a damaging move in place of Heal Pulse to take them out.