I have been thinking about this, and I have come up with a new nuzlocke variant. It's called the Matchuplocke.

The rules:

It has the standard nuzlocke rules,

-A pokemon that faints is considered dead and must be released or put in a death box.
-Nickname all your pokemon.
-Only catch the first pokemon 'possible' to catch on each route/area you encounter. If you kill it, to bad.

Now what do I mean by 'possible'? This variant has some extra rules:

-At the beginning of the game, you pick a type. Do this by randomizing a number between 1-17. 
1=Fire
2=Water
3=Grass
4=Electric
5=Psychic
6=Dark
7=Normal
8=Dragon
9=Ghost
10=Ice
11=Fighting
12=Ground
13=Rock
14=Steel
15=Bug
16=Poison
17=Flying

If the type you end up getting, for example, is fire, I can only use types that are either not very effective or super effective against it. In this case, the types I can use in the Matchuplocke are water, ground, rock, grass, steel, bug, ice, and fire itself. (note, I can use fire because fire is not very effective against fire)  In other words, if you get normal, you're screwed.

If none of your available types are obtainable before gym no.1, you may get a new chance.

Personal rules, that I like to apply:

-Game on set mode
-No dupe clause
-Don't overgrind, except for e4 and champion
-If you already have a team of six, you can't receive gift pokemon for your type, like eevee
-Speaking of eevee, you may get an eevee if your type was fire, but only if you evolve it into vaporeon, leafeon, flareon or glaceon

That's about it, hope you like it and you may add additional rules to it

FunnyFurret : Seems to be a good Nuzlocke idea,
I'm not really a ''Fan'' of that kind of playing but this idea seems to be fun, and more difficult in my opinion.
Are you going to try this out Furret?

Oh, so creative! This is a very nice idea for a nuzlocke! I will try it, and see if I can get through it. 

Oh, this is cool and I think it is unique from the other way of doing  a nuzlocke. I want to try doing one, but I am going to do it this way instead. I think this is cool and I have always wanted to do one. But I like your rules man. This is awesome! Very creative! Nice job with this I am definitely going to try it out!