"Sie möchten, dass du keinen Fisch isst."
They would like that you do not eat "any" fish.
i thought keinen means "not any"
"Any" is not necessary here. "Don't eat fish" and "Don't eat any fish" is almost the same. In fact, if you translate this literally, you'll get "They would like that you eat no fish". "Not any" seems a little more emphasized than that. I usually think of "kein" like of "no" and then try to make the English sentence more natural.
Yes, "that" used as a conjunction is "dass" in German.
Okay, I wasn't aware that there was a difference in the way you spell it! My spell checker in firefox actually underlined "dass" as if it was wrong!