Alright, my consideration of a Doubles team has led me to this. I'm fond of Water Pokemon, and I'm fond of the idea of a Rain Dance team, so I'm about to start constructing this team for use in the tournament, unless somebody can point out some glaring flaw in it. Remember, six Pokemon total (but each match is 4 on 4), Item Clause, but you can choose your four Pokemon before each match, and switch the six items around if necessary.
Kingdra - Swift Swim @Life Orb
Modest, 240 HP/252 SpA/16 Spe
-Surf
-Ice Beam
-Dragon Pulse
-Signal Beam/Rain Dance/Filler
My potential sweeper. Plenty of type coverage, fast, resistances with only one weakness. Life Orb gives it an expiration date, but will let it hit even harder than before. The fourth move is mostly me grasping at straws, but ideally I'd like to have three Rain Dancers on the team, to give me more variety in my lineup. Kingdra can fill in for one of those slots if necessary (more details below).
Lapras - Water Absorb @ Leftovers
Modest, 164 HP/92 Def/252 SpA
-Surf
-Thunderbolt
-Ice Beam
-Toxic/Filler
Lapras is one of my favorite water Pokemon, but it's one that I rarely get to use. I plan to make full use of Water Absorb here, and if I can pair Lapras up with one of my other Water Absorb/Dry Skin Pokemon, even better, as they'll be able to keep themselves alive. Leftovers can only help here. Thunderbolt and Ice Beam give even more type coverage, with STAB on the latter, to make Lapras a powerful force. Toxic provides PHazing, although I'm not averse to another move here. I just...don't know what else.
Vaporeon - Water Absorb @ ?
Bold, 188 HP/252 Def/68 SpA
-Surf
-Ice Beam/Wish
-Shadow Ball
-Yawn
Does Wish pass over without a Baton Pass? I forget. If so, it might be a nice way for Vaporeon to provide some support if it gets low on health. Shadow Ball is there for Shedinja coverage, Yawn for PHazing. Surf lets Vaporeon match up with Lapras or Toxicroak very nicely. I'm not sure on an item for Vaporeon--this is a case where I'd probably swap one of the other items in. Suggestion?
Toxicroak - Dry Skin @ Black Sludge
Jolly, 18 HP/252 Atk/240 Spd
-Substitute
-Focus Punch/Cross Chop
-Sucker Punch
-Stone Edge
When I saw this set suggested earlier in the thread, the entire team came together for me. I love the idea of Toxicroak--it seems like a wild card to the Rain Dance idea, but will thrive in it, and what's more, it can be very versatile while still being a very solid Pokemon. I can match it up with any of the Surf users for great success, although that's not really even necessary if Rain Dance is up--Toxicroak will thrive even then, Surf is just for added insurance. That actually makes me curious--would a healing Surf break Toxicroak's Substitute? That could be a big factor. Sucker Punch gives me priority and Shedinja coverage. I'm undecided between Focus Punch and Cross Chop--the former is more powerful and works well with Substitute, but concerns were raised over that. Opinion?
And then two of the following three, to be decided:
Ludicolo - Swift Swim @ Damp Rock/Big Root
Calm, 204 HP/76 SpA/124 SpD/104 Spd
-Fake Out
-Hydro Pump
-Grass Knot/Giga Drain
-Rain Dance/Leech Seed
Fake Out is a useful attack for an emergency. Hydro Pump is my major damage attack, and the latter two moves depend on which set I want to go with. Rain Dance and Grass Knot is more traditional, but I'm intrigued by the potential of Giga Drain, Leech Seed and Big Root, and how long that could keep Ludicolo in play.
Aerodactyl - Pressure @ Chilan Berry/Damp Rock
Jolly, 4 HP/252 Atk/252 Spe
-Taunt
-Foresight
-Rain Dance
-Rock Slide
Somebody posted an anti-Lead Aerodactyl, and that intrigued me enough to consider adding it here. I love the idea of throwing a Foresight in to screw up a foe's Ghost+Explosion tactic, especially as the foe explodes--one of their Pokemon will fall without it being expected. Aerodactyl's Rock type, plus the Chilan Berry, should let it survive the Explosion with relative ease. From there it should be easy to set up Rain Dance, and then hit with Rock Slide for as long as possible. Taunt is there to fight off a Trick Room or something like that.
Omastar - Swift Swim @ Damp Rock/Chilan Berry
Modest, 4 Def/252 SpA/252 Spe
-Rain Dance
-Hydro Pump
-Ice Beam/Knock Off/Stealth Rock/Protect/Ancientpower
-Ice Beam/Knock Off/Stealth Rock/Protect/Ancientpower
Omastar is a Pokemon that kept jumping out at me here. It didn't fit into my team at first, but it kept showing up whenever I was thinking about the team, prompting this three-way debate. It can work similarly to Aerodactyl with the Explosion absorbing (Rock type plus Chilan Berry) and setting up Rain Dance, while still thriving in a Rain Dance environment, should it survive past the setup. The last two attack are basically a toss-up--I could bank on it not surviving much longer anyway and set up Stealth Rock to hopefully cripple new opponents as they come out, or I could hope to find a good item to Knock Off to cripple an opponent that way, or I could give it Protect to increase survivability, or Ice Beam and Ancientpower if I wanted to try sweeping with it anyway. Either way, Hydro Pump is a necessity, as with luck I can get out at least one full-powered shot after setting up Rain Dance.
So there you have it, my team. Of the final three Pokemon, I need to bring the Damp Rock into battle somehow. The more I think about it, the more I think that Ludicolo will wind up going the Rain Dance route, forgoing the Big Root strategy, but I'm not sure. EVs are also still up in the air--some were cribbed from the Smogon strategies, others from this thread, and I'll likely have to modify them a bit as I build my team. Opinions? On all of it? Or would this be better in a RMT topic?

Kingdra - Swift Swim @Life Orb
Modest, 240 HP/252 SpA/16 Spe
-Surf
-Ice Beam
-Dragon Pulse
-Signal Beam/Rain Dance/Filler
My potential sweeper. Plenty of type coverage, fast, resistances with only one weakness. Life Orb gives it an expiration date, but will let it hit even harder than before. The fourth move is mostly me grasping at straws, but ideally I'd like to have three Rain Dancers on the team, to give me more variety in my lineup. Kingdra can fill in for one of those slots if necessary (more details below).

Lapras - Water Absorb @ Leftovers
Modest, 164 HP/92 Def/252 SpA
-Surf
-Thunderbolt
-Ice Beam
-Toxic/Filler
Lapras is one of my favorite water Pokemon, but it's one that I rarely get to use. I plan to make full use of Water Absorb here, and if I can pair Lapras up with one of my other Water Absorb/Dry Skin Pokemon, even better, as they'll be able to keep themselves alive. Leftovers can only help here. Thunderbolt and Ice Beam give even more type coverage, with STAB on the latter, to make Lapras a powerful force. Toxic provides PHazing, although I'm not averse to another move here. I just...don't know what else.

Vaporeon - Water Absorb @ ?
Bold, 188 HP/252 Def/68 SpA
-Surf
-Ice Beam/Wish
-Shadow Ball
-Yawn
Does Wish pass over without a Baton Pass? I forget. If so, it might be a nice way for Vaporeon to provide some support if it gets low on health. Shadow Ball is there for Shedinja coverage, Yawn for PHazing. Surf lets Vaporeon match up with Lapras or Toxicroak very nicely. I'm not sure on an item for Vaporeon--this is a case where I'd probably swap one of the other items in. Suggestion?

Toxicroak - Dry Skin @ Black Sludge
Jolly, 18 HP/252 Atk/240 Spd
-Substitute
-Focus Punch/Cross Chop
-Sucker Punch
-Stone Edge
When I saw this set suggested earlier in the thread, the entire team came together for me. I love the idea of Toxicroak--it seems like a wild card to the Rain Dance idea, but will thrive in it, and what's more, it can be very versatile while still being a very solid Pokemon. I can match it up with any of the Surf users for great success, although that's not really even necessary if Rain Dance is up--Toxicroak will thrive even then, Surf is just for added insurance. That actually makes me curious--would a healing Surf break Toxicroak's Substitute? That could be a big factor. Sucker Punch gives me priority and Shedinja coverage. I'm undecided between Focus Punch and Cross Chop--the former is more powerful and works well with Substitute, but concerns were raised over that. Opinion?
And then two of the following three, to be decided:

Ludicolo - Swift Swim @ Damp Rock/Big Root
Calm, 204 HP/76 SpA/124 SpD/104 Spd
-Fake Out
-Hydro Pump
-Grass Knot/Giga Drain
-Rain Dance/Leech Seed
Fake Out is a useful attack for an emergency. Hydro Pump is my major damage attack, and the latter two moves depend on which set I want to go with. Rain Dance and Grass Knot is more traditional, but I'm intrigued by the potential of Giga Drain, Leech Seed and Big Root, and how long that could keep Ludicolo in play.

Aerodactyl - Pressure @ Chilan Berry/Damp Rock
Jolly, 4 HP/252 Atk/252 Spe
-Taunt
-Foresight
-Rain Dance
-Rock Slide
Somebody posted an anti-Lead Aerodactyl, and that intrigued me enough to consider adding it here. I love the idea of throwing a Foresight in to screw up a foe's Ghost+Explosion tactic, especially as the foe explodes--one of their Pokemon will fall without it being expected. Aerodactyl's Rock type, plus the Chilan Berry, should let it survive the Explosion with relative ease. From there it should be easy to set up Rain Dance, and then hit with Rock Slide for as long as possible. Taunt is there to fight off a Trick Room or something like that.

Omastar - Swift Swim @ Damp Rock/Chilan Berry
Modest, 4 Def/252 SpA/252 Spe
-Rain Dance
-Hydro Pump
-Ice Beam/Knock Off/Stealth Rock/Protect/Ancientpower
-Ice Beam/Knock Off/Stealth Rock/Protect/Ancientpower
Omastar is a Pokemon that kept jumping out at me here. It didn't fit into my team at first, but it kept showing up whenever I was thinking about the team, prompting this three-way debate. It can work similarly to Aerodactyl with the Explosion absorbing (Rock type plus Chilan Berry) and setting up Rain Dance, while still thriving in a Rain Dance environment, should it survive past the setup. The last two attack are basically a toss-up--I could bank on it not surviving much longer anyway and set up Stealth Rock to hopefully cripple new opponents as they come out, or I could hope to find a good item to Knock Off to cripple an opponent that way, or I could give it Protect to increase survivability, or Ice Beam and Ancientpower if I wanted to try sweeping with it anyway. Either way, Hydro Pump is a necessity, as with luck I can get out at least one full-powered shot after setting up Rain Dance.
So there you have it, my team. Of the final three Pokemon, I need to bring the Damp Rock into battle somehow. The more I think about it, the more I think that Ludicolo will wind up going the Rain Dance route, forgoing the Big Root strategy, but I'm not sure. EVs are also still up in the air--some were cribbed from the Smogon strategies, others from this thread, and I'll likely have to modify them a bit as I build my team. Opinions? On all of it? Or would this be better in a RMT topic?