Well, Challenge Cup is completely about luck so I can't give you any advice on that, but for Little Cup I'd suggest the following Pokémon:
Gastly @ Przcureberry
- Giga Drain
- Thunder
- Psychic
- Filler move
Elekid @ Gold Berry
- Thunderpunch/Thunderbolt/Thunder (whichever is the easiest to get)
- Quick Attack
- Cross Chop (which you'll have to breed for)
- Light Screen/Filler
Ponyta @ Berry
- Double Kick
- Fire Blast/Flamethrower (whichever is easier to get)
- Iron Tail/Filler
- Agility/Filler
Dratini @ whatever
- Dragon Rage (just breed a male Dratini/Dragonair/Dragonite with Dragon Rage with a female Dratini/Dragonair/Dragonite with Dragon Rage and the baby will have it. I'm not sure, but just having Dragon Rage on the male one might be enough, too.)
- Filler
- Filler
- Filler
Dragon rage is really all you need as it'll OHKO everything in Little Cup apart from that Chansey that appears in one round.