Wow. Lots of harsh comments here.
About not running Claydol and Uxie:
Saying "I hate how everyone is using Claydol and Uxie!!!!!" is stupid. I'm sorry, but it's just true. That's like saying I hate how everyone is using Bebe's Search! Or Roseanne's Research! I hate how every SP deck runs Poke-Turn and SP Radar! I hate how every deck runs ENERGY! I hate how - okay, you get the idea. Most of the time the people who have a distaste for Claydol and Uxie are saying that to make themselves feel better about not having them.
Not using Claydol or Uxie is silly. I understand you wanting to come up with a deck combination/idea yourself, but there comes a point where you have to stick to a basic template - an idea that others have found works. That template is almost always a Claydol line, 1-3 Uxie, 4 Bebe's, and 4 Roseanne's. If you don't have those, your deck won't be consistent unless you have some wacked-out way of drawing cards (see Scizor/Cherrim) and even then it will be iffy at best compared to the Claydol players.
If you have Claydols and Uxies, run them. Not running them is like having dice to use for damage counters, but preferring to use those silly paper ones, because "it's more authentic" or, more correctly, "everyone else is using them". They're using them because they're the best tools available for what they need to do. It's like saying you prefer using a rock to hammer in a nail - instead of a hammer, because everyone else uses hammers. You know what I mean? Just buckle down and do it. It's okay. We won't look down on you for it.
(Edited in: "I beleive that if a deck is good enough you should be able to win even if you are at a disadvantage." You need to know that this statement makes no sense and any interpretation I come up with is completely false. If you are at a disadvantage, you are losing. You can never guarantee a win under such circumstances. Further, and more on topic, if you're at a disadvantage because you can't get any critical cards out, it doesn't matter how good your deck is - though it's probably not all that good to begin with!)
To actually give you an answer, though. I honor that you don't want to run Claydol or Uxie (Or, you don't have them). Here are my ideas.
There are two options I can give you.
1. Run a different type of draw engine. The only one I know of is Porygon-2 GE + Staraptor FB Lv. X, with Professor Oak's Visit and/or Felicity's Drawing. That's the best draw system I know outside of Claydol and Uxie. Other than that, you can try Solrock SV + Lunatone GE, where you can check the top three cards of your deck, put one on top, and then discard a card from your hand to draw it. These won't be as fast as Claydol, but they will work.
2. Run a deck that doesn't need a Pokemon-based draw engine. My current league owner makes decks that consist of 12-20 energy, 20-26 trainers, and 6 Pokemon or so. Such an absurdly focused deck NEVER needs Claydol - he sets up with no problems at all. Use 4/4 Bebe's/Roseanne's, then Quick and Dusk Balls (prefer Quick if you're short on space). You can't have a complex setup with this, but my LO can make a Darkrai swarm deck that's actually rather effective this way - a little slow, granted, but effective. He also ran Butterfree GE + Shaymin Lv. X (both).
And SECRET OPTION NUMBER THREE:
3. ARCEUS [del]IS NOT A MEME[/del] DOESN'T USE CLAYDOL/UXIE