You're going about this all wrong. The negative claim (fairies don't exist) cannot exist without the positive claim (fairies do exist) being made first. You can't say that you don't believe in god unless someone first makes the claim that god does exist. The claim and burden of proof both fall on the "god exists" camp.
Your claim that you need to argue that something exists before you can argue that it doesn't exist is manufactured hogswash to try and shift the burden of proof onto the theist camp. If you have to try and set up conditions at the start of a debate where your opponent has to do more work than you do that's a pretty good indicator that your argument itself is pretty weak.
In actual logic there's no reason at all that you have to argue for something to exist before you can argue against it.
Person A: Here's a definitino for God. [Provides a definition.]
Person B: So do you believe God exists?
Person A: Nope. I just think it's an interesting concept.
Person B: Well, I think God doesn't exist. [Provides reasoning.]
You see how it was totally unnecessary to say God exists before arguing that He doesn't? All that is necessary is a definition so you have a concept to argue about.
The claim is that god exists, not that he doesn't exist. Person A says to Person B, I believe god exists. Here's why. Person B says, your evidence is not sufficient enough to support your claim. Person B is not making a claim. He is rejecting the claim made by Person A based on lack of evidence.
You are either deliberately employing sleight of hand to try and build your case, or you simply haven't grasped the distinction between strong (positive) and weak (negative) atheism. Here are the definitions again:
Strong atheism is a term generally used to describe atheists who accept as true the proposition, "gods do not exist". Weak atheism refers to any other type of non-theism. Historically, the terms positive and negative atheism have been used for this distinction, where "positive" atheism refers to the specific belief that gods do not exist, and "negative" atheism refers merely to an absence of belief in gods.
http://en.wikipedia.org/wiki/Weak_and_strong_atheism
So, if Person B understood logic and was honest, this is how the conversation would play out.
Person A: I believe in God. [Presents reasoning.]
Person B: I find your reasoning unconvincing, so I fail to accept your conclusion. I do not believe in God. (WEAK ATHEISM)
Person A: So you believe God doesn't exist? (STRONG ATHEISM)
Person B: Not necessarily. If I wanted to make a positive claim that God doesn't exist (STRONG ATHEISM) I'd have to build an argument to do so. I don't feel like doing that. So I'm just going to observe that your reasoning is weak, fail to accept your conclusion, and be content with disbelief regarding God (WEAK ATHEISM) rather than belief that He does not exist (STRONG ATHEISM).
You might also notice that I'm saying "fail to accept" rather than "reject". This is also basic logic. If an argument is invalid (e.g. the conclusion doesn't follow from the premises) or unsound (e.g. some of the premises are not true) than you can reject the argument. You can not, however, reject the conclusion. You can simply say that the argument didn't prove the conclusion. The conclusion may or may not be true by some other reasoning.
For example:
1. The American flag is red, white and blue.
2. All flags with the color red in them are constitutional republics.
C. America is a constitutional republic.
Premise 2 is obviously false so the argument is unsound. But if you were to conclude that because the argument is unsound the conclusion must be false you'd be making your own logical error. So if someone presents an argument from God and you observe that the argument doesn't work you can't automatically assume the conclusion is false (STRONG ATHEISM). You can only observe that they haven't proved their case, so you have no reason to believe them (WEAK ATHEISM).
This is all basic logic, and it boils down to the original point: If you make a claim - any claim - you have the burden of proof. Weak atheism doesn't make a claim. It just rejects someone else's argument. That's why it's called negative atheism. Strong atheism does make a claim. It states that the universe is actually a certain way (e.g. devoid of God). That is the reason it is often called positive atheism.
Pick which one you are. If you're a weak atheist then great. You don't have a burden of proof. But if you're a strong atheist (which most of the annoying, trendy atheists like Richard Dawkins are) then you damn well do have a burden of proof.