EDIT: After losing to only the 27th trainer, I've decided to use my other pokemon. Although it took hours to breed and train my Lopunny, I finally got it. Here is my overhauled team...
2nd EDIT: Another change, hopefully will give me much better results...
Lopunny, in a way, outclasses her fellow psychic legendaries. She isn't affected by choice scarf, so she can use thunder wave and charm freely to cripple any pokemon in case she gets a choice item. Ground types who resist thunder wave would hate to be charmed, while specially-based pokemon won't like being paralyzed or captivated. The only pokemon who wouldn't mind either is Claydol, female Electivire, female Lanturn, and female Jolteon, though they would not enjoy choice scarf either. Lopunny can take hits reasonably well, with base 84 defense and 96 special defense. She functions well even without the effects of choice scarf, thanks to base 105 speed.
2nd EDIT: Another change, hopefully will give me much better results...
Lopunny @ Choice Scarf
Ability: Klutz
Nature: Jolly
EVs: 252 HP/ 4 SpD/ 252 Spe
~Switcheroo
~Thunder Wave
~Charm
~Captivate

Ability: Klutz
Nature: Jolly
EVs: 252 HP/ 4 SpD/ 252 Spe
~Switcheroo
~Thunder Wave
~Charm
~Captivate
Lopunny, in a way, outclasses her fellow psychic legendaries. She isn't affected by choice scarf, so she can use thunder wave and charm freely to cripple any pokemon in case she gets a choice item. Ground types who resist thunder wave would hate to be charmed, while specially-based pokemon won't like being paralyzed or captivated. The only pokemon who wouldn't mind either is Claydol, female Electivire, female Lanturn, and female Jolteon, though they would not enjoy choice scarf either. Lopunny can take hits reasonably well, with base 84 defense and 96 special defense. She functions well even without the effects of choice scarf, thanks to base 105 speed.
Drapion @ Black Sludge
Ability: Battle Armor
Nature: Careful
EVs: 252 HP/ 56 Def/ 196 SpD/ 4 Spe
~Crunch
~Acupressure
~Rest
~Sleep Talk

Ability: Battle Armor
Nature: Careful
EVs: 252 HP/ 56 Def/ 196 SpD/ 4 Spe
~Crunch
~Acupressure
~Rest
~Sleep Talk
Jumpman16, I hope you did well in business school. Opted for sleep talk rather than substitute, since it is a pain to get 2000 coins in HG/SS. This set actually performs phenomenally! Continuous rest and sleep talk to get several acupressures makes Drapion define a new tier above the ubers. Crunch is the attacking move, since nothing is immune to it. In addition, battle armor prevents the critical hit hax.
Swinub @ Focus Sash
Ability: Oblivious
Nature: N/A
EVs: N/A
~Endeavor
~Ice Shard
~Fissure
~Endure

Ability: Oblivious
Nature: N/A
EVs: N/A
~Endeavor
~Ice Shard
~Fissure
~Endure
This set is specifically used to counter OHKO moves. With an immunity to sandstorm and hail, Swinub can always bring one pokemon down with it that isn't a ghost. As a last resort, fissure is used for non-levitating ghost pokemon, which would only hit Dusknoir, Sableye, Froslass, Banette, and Spiritomb, should Swinub be the last pokemon. Swinub is also a badass.