Well it won't do as well as others, but it can still be effective for some rounds. EV and IV stats are very important in the Battle Tower. Perfect max IV preferably.
1. Espeon @Choice Scarf
Ability: Synchronize
Nature: Bold / Impish
EV: 252 HP, 252 Defense, 6 Speed
~ Trick
~ Yawn
~ Flash
~ Charm
Definitely one of the faster Eeveelutions. Access to Trick, Flash, and Charm are great moves to have in the Battle Tower. Be sure to Trick first turn or else, you will waste a turn with Choice Scarf forcing you to use Trick. After you lock the opponent into using that one move, choose the move that is right. If it is a physical move, use Charm. Special move, use Flash or Yawn. Morning Sun is a decent option if you need to heal. The bad news is that Espeon has no move like Thunder Wave to dispel the effects of Choice Scarf. Use Yawn to put it to sleep so Vaporeon and Leafeon can have some setup time.
2. Vaporeon @Leftovers
Ability: Water Absorb
Nature: Bold
EV: 252 HP, 128 Defense, 128 Speed
~ Baton Pass
~ Acid Armor / Heal Bell
~ Substitute
~ Icy Wind
Vaporeon works good decently after Espeon and if the opponent's lead is not a Grass or Electric type. Acid Armor to raise her Defense. Substitute to make sure that your opponent cannot status Vaporeon. And if Jolteon's Trick Choice Scarf, you probably want to just use Substitute, then Heal Bell and use Icy Wind to hope in dispelling Choice Scarf. After that, Baton Pass to Leafeon, passing over Substitute. Acid Armor is nice too if you can time Yawn with Espeon. If not, Heal Bell.
3. Leafeon @Life Orb
Ability: Leaf Guard
Nature: Jolly
EV: 6 HP, 252 Attack, 252 Speed
~ Swords Dance
~ Leaf Blade
~ Double-Edge / Return
~ Synthesis
An attacker. She is under-appreciated, but she has decent speed with great Attack power and very high Defense. Power up with Swords Dance and sweep.
I think it's decent. Shame that it only has ONE attacker, but there's not a whole lot that we can do. Leafeon should hope to get in 3 Swords Dance. Another problem is that none of the Eeveelutions are immune to Thunder Wave, Will-O-Wisp (Flareon sucks), or Toxic. This makes it hard to set up properly (and necessary to have Vaporeon).
Lastly, don't run a Toxic stall team. You will LOSE in the Battle Tower. Especially with no recovery moves and it has no effect on Steel- or Poison-type Pokemon.
Hope this helps.