Decklist from James Arnold.
Additional reading from Tablemon (in the context of the 2005 format).
This deck attacks with Nidoqueen, a bulky 120 HP Stage 2 Pokémon. Toxic costs {G} and does 40 damage per turn cycle, though you cannot stack this damage. Power Lariat has a floor of 40 damage, assuming you have no other Evolved Pokémon in play and Double Rainbow Energy is attached, but can do as much as 100 damage if you are completely set up.
Pidgeot is the setup Pokémon/secondary attacker. The deck runs 3-2-3 Pidgeot instead of the usual 2-1-2 or 2-0-2, since Nidoqueen rewards you for having more Evolutions in play.
Lead with Nidoran ♀ and use Look for Friends and/or Great Ball to set up Basic Pokémon. Celio's Network will find either Nidorina or Pidgeot, which you then chain into more Evolution searches. Continue building your board until you are ready to go on the offense, which can happen at any time. Nidoqueen's Toxic costs just 1 Energy, so it's easily paid for if you already have a Nidoran ♀ using Look for Friends (with Rare Candy to jump straight to Nidoqueen), or a Nidorina using Fast Evolution with Double Rainbow Energy attached. DRE doesn't reduce Toxic's damage output either, which is nice.
You can give up five Prizes, and you have 4 Nidoqueen, so you can throw a Pidgeot into the mix as a wall/attacker. Don't underestimate Pidgeot's combat capabilities, and don't worry about losing Quick Search — you play a thicker Pidgeot line than most other decks, so you should be able to build a second Pidgeot if the first is KOed.
This deck doesn't use the Holon Engine, instead relying on Nidoran ♀ and Nidorina's attacks and Great Ball to set up. For this reason, I prefer thick 4-3-4 and 3-2-3 lines. Nidorina is more than just a step on the path towards Stage 2; it helps build your board with its Fast Evolution attack, so 3 copies is worthwhile. 2 Pidgeotto means it's less likely for all copies of it to be Prized and for Fast Evolution to whiff on it.
As this deck plays 3-2-3 Pidgeot, turboing out a turn 1 Pidgeot is more likely compared to other decks that play 2-1-2. You also have Double Rainbow Energy to begin attacking. I have donked opponents that started with Dratini (weak to Colorless) off a T1 Pidgey -> Rare Candy -> Pidgeot -> Double Rainbow Energy.
Holon's Magneton can be used to replay Heal Energy, or to remove the -10 damage drawback on Double Rainbow Energy at the cost of your Energy attachment for the turn.
Try to hold Nidoqueen in hand if you think your opponent is going to put a Special Condition on you. When they do, evolve to Nidoqueen to clear it. You don't have to rush Nidoqueen out; if your opponent doesn't pull the trigger, you can continue setting up your board with Nidoran ♀ and Nidorina's attacks.
Nidorina and Nidoqueen have different types and Weaknesses. Most of the time this is of little relevance, since Power Lariat hits for at least as much as Scratch, even if the former is resisted or the latter is super-effective.
Nidoqueen δ, Pidgeot δ: Tech options, since you already play the necessary pre-evolutions. You need to add Holon Energy for Pidgeot δ.
Milotic: Tech from the 2005 format. It wins damage races against spread damage or ex decks, and can also provide a reprieve against Cursed Stone damage on Pidgeot (though you should still get rid of the Cursed Stone quickly, as otherwise Milotic will take damage too!). One important interaction is that if they use Ancient Technical Machine [Rock] to devolve your Pokémon, you can play Milotic and heal all damage again.
Nidoqueen is not completely walled by Resistance, as Toxic allows it to chip down opposing Pokémon that resist Power Lariat.
Toxic also has the advantage of stopping Poké-Powers. If you manage to assemble a Nidoqueen while your opponent is still on Jirachi, Toxic puts a very fast clock on it and prevents it from using Wishing Star. Another scenario: if your opponent sends out Pidgeot to wall Power Lariat, you just Toxic it and they can't use Quick Search.
This deck is fairly resilient against Pow. Pidgeot has 0 Retreat, as do Nidoran ♀ and Nidorina if Nidoqueen's Poké-Body is active. The Energy-moving mode of Pow can still mess you up by transferring Double Rainbow Energy onto a Basic (whereupon it gets discarded), but you can play around it by not leaving exposed Basics on your Bench, or through it by Quick Searching up another DRE, or simply attacking with Toxic since it costs just 1 Energy. Not playing dedicated setup Pokémon like Jirachi or Lapras helps, as you won't have those dead weight Bench sitters presenting themselves as Pow targets.
If Crystal Beach is in play, you're color screwed off Power Lariat. You need to use Windstorm or Desert Ruins to remove it; failing that, your only out is the 1-of Fighting Energy.
Rayquaza δ is a unwinnable matchup unless you get extremely lucky. Rayquaza δ resists Fighting, and once it gets Holon Energy WP attached, it loses its Weakness to Pidgeot and can't be poisoned.
This is a matter of personal taste, but this deck can feel a bit too "honest" in the RS-PK format. The most broken thing you're doing is Quick Searching with Pidgeot, which is nothing special, a ton of other decks also do that. You don't have Pow, you don't have Cessation Crystal, you don't have Energy acceleration outside of Double Rainbow/Scramble providing more than 1 Energy, you're not even running the Holon Engine (though with good reason; you don't have a lot of discard fodder). Nevertheless, this deck is still viable; in fact Jason Klaczynski considers it a "top deck"!