Re: CAN't vs DON't
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'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.