How about "я не тебе верю"?
Hm i think that that would mean "i believe someone else, not you"
Why тебе and not тебя? Wouldn't I do not love you be я не тебя люблю, or have I gotten it wrong?
Верить is one of the verbs that uses the Dative.
It is a song, one of my favourite russian songs with this name "Я тебе не верю"