burden of proof on the god question rests with the theist. Still, I have seen more than a few atheists get sucked into the trap of a theist asking for proof of atheism. In this post, I will suggest that there are at least two reasons for not seriously entertaining requests for such proof of atheism.
Burden of Proof
Anyone who has taken even an introductory course in philosophy will tell you that the burden of proof always rests with the side making the claim. The theist claims that there is some sort of god; the atheist does not accept this claim (usually due to a lack of sufficient evidence). The burden of proof belongs to the theist. If you want us to believe that your god(s) exist, make your case by providing evidence sufficient to support the claim.
Educated believers generally accept this burden but attempt to sidestep it through faith. Since they realize that there is insufficient evidence to support their god claim, they resort to faith. Some even try to turn faith (i.e., the acceptance of a claim without sufficient evidence) into a virtue of sorts.
Less educated believers may actually ask atheists to prove that no gods exist. In such cases, it may be necessary to teach them about the burden of proof and use examples with which they can relate. It may also be necessary to help them understand what atheism means in the first place. With patience, it is often possible to show them that their request was misplaced.
The Role of Proof in Evaluating Religious Claims
In addition to helping the theist understand his or her burden of proof, it is often helpful to consider that "proof" might not even be the correct standard here. I would argue that the problem with believing that some god or gods exist is not that the existence of such a beings cannot be proven; the problem is that there is insufficient evidence to justify the belief.
Not all atheists will agree with this, so let me be clear about what I am saying here. I can accept the idea that someone could believe something without having absolute proof in the object of one's belief. As long as the evidence adequately justifies the claim, it need not rise to the level of proof in all cases. Clearly, this means that the nature of the evidence needed will vary with the type of claim being made.
If I claim that I regularly walk to my mailbox to get the mail without wearing shoes, you may just take my word for it and require minimal evidence. On the other hand, you are right to ask for considerable evidence to support my claim that a supernatural being punishes sinners with hurricanes while rewarding homophobia with Republican votes.
The bottom line is that atheists need not entertain requests for proof of atheism from believers. It is they who have the burden of proof, and if not proof, then sufficient evidence to justify their claims. That they they have been unable to come close to meeting such a burden is all the "proof" atheism needs.