CAN't vs DON't

This is not a grammar question but rather a question about context or actual usage.

1, I can't believe you!
2, I don't believe you!

What context would you imagine?
To what statement or scene should they be said well, does one fit better than the other?

I am asking this because generally Japanese students tend to use "can't" too often, even when "don't" matches better.
So, I want to know a lot of situations where each of these really fits well, including these two can be used interchangeably.

Thank you in advance.

I think "I don't believe you" would apply about 95% of the time. (Wild guess on the number.)

To me, "I can't believe you" means "I don't think you are telling me a deliberate lie, and maybe I would like to believe you, but it's impossible for me to accept this as the truth." (It would be the same if you didn't want it to be the truth.)

I would use 'don't'. The other way sounds odd...