As the Little Cup metagame is played at level 5 rather than the usual level 100, there are some unique difficulties in fully EV training a Pokémon without bringing it over the level 5 limit.
"Spare" EXP before you hit Level 6
Each Pokémon has a Base EXP rate which determines how quickly it levels up.
Pokémons's EXP can be determinated in Flucating, Slow, Medium Slow, Medium Fast, Fast and Erratic.
Calculate how much EVs you will won
To know how many battles you will need, and therefore how many EXP you can afford to gain per battle (and whether you need Pokérus) it is advised that you perform a calculation to check how many EVs you will need to gain in battle.
Minimizing EXP Gain Per Battle
Since you will be gaining most of your EVs via Power Items, it's best to just look for Pokémon that give few EXP per battle, unlike the EVing hotspots used for normal EV training. Wild Magikarp give the lowest EXP of any Pokémon that can be found, and are easy to find, even if fishing is slightly slow. Simply fish anywhere with the Old Rod.
What this means, is that you need to battle with pokémons that give you low experience and of course, at a low level.
Great things to have
Pokérus, Power Items, Vitamins or Wings and having 31 IVs is perfect.
Hotspots for Little Cup EV Training in XY
HP - Caterpie (Pokémon Y Route 2), Azurill (Route 3)
Defense - Scatterbug (Route 2)
Special Attack -
Special Defense -
Speed - Bunnelby (Route 2), Fletchling (Route 2)
I didn't find Attack, Sp.Atk and Sp.Def spreaders with low level, but if I find, I will tell.
You can EV training in other game.
EV training for Atk, Sp.Atk and Sp.Def in other games
Attack - Patrat (BW2 at Route 19)
Special Attack - Sunkern (BW2 at Route 20)
Special Defense - Still didn't find.
Pokéradar, Hordes, Super Training, EV training in other games them Pokébank it (see up).