It's "...do you not like".

I suppose the answer is that the negation of "to like" is "not to like". So, in the present tense, the negation of "like" is "not like". The correct word order is therefore "...do you not like".

However, as you quite rightly point out, it *IS* abbreviated to "don't you like". That does make sense if you regard "don't" as a separate word. (There's no such word as "doyoun't"). You can't put one word inside another word (except in very unusual circumstances), so if you're going to use "don't" it will have to go either one side or the other of "you". It definitely can't go after the "you" because that would completely change the meaning, so the only option left is before.

Curiously, "...do not you like" is probably not actually formally incorrect, just very, very unusual.

Rommie