It appears you understood better than I orignally thought

I would like to clear up one thing though.
That *is* the definition of being an atheist, whether I believe in deities or not does not change the definition. As I mentioned, I do believe in deities.
That *can not* be the definition of being an atheist, because one cannot support the assertion that God does not exist.
Incorrect. The burden of proof lies with the one making the positive assertion (in other words, the one who believes in deity must prove its existence). It is a logical fallacy to prove a negative. For example, prove to me the flying purple unicorn from Uranus does not exist. Just because you can't prove it exists does not mean that it does.
You are correct that the burden of proof lies with the one making the postive assertion; the postive assertion here is that
God does not exist. You are absolutely right, except for what you have said about the burden of proof. Here, it correctly lies on the postive assertion
God does not exist. Since one cannot prove the nonexistence of something, the defintion of atheism(the belief that God does not exist) is illogical. That is why I said that your defintion of atheism is wrong; Atheism is properly defined as
the lack of belief in the existence of God.
Postive Assertion(which is unprovable):
the belief that God does not exist
Negative Assertion(correct definition of atheism):
the lack of belief in the existence of God
The difference is subtle, but it is there. The former is taken on faith, while the latter is an absence of faith.
Atheism seems pretty logical to me - why believe in something without [convincing] evidence? Do you believe in the flying purple unicorn from Uranus? why or why not?
I agree. I do not beleive there exists a flying purple unicorn from Uranus. However, to assert that the flying purple unicorn from Uranus does not exist is illogical. To support my assertion that this unicorn does not exist, I would need evidence of it's non-existence, as the burden of proof lies with the postive assertion(which I am making when I say it does not exist!).