It could rain tomorrow. means that it is possible that it will rain. The modal verb 'could' expresses possibility.
The negative would normally be expressed by "It couldn't possibly rain tomorrow." (we're in the desert!) or "It's not possible that it will rain tomorrow." (we've had rain for 40 days and 40 nights, and it's ludicrous to add on another day of rain!) or by the opinion, "I don't think it will rain tomorrow."
So, the sentence, "It could rain tomorrow." means "It is possible that it will rain."
Therefore, the question, "Is it possible for it to rain tomorrow?" and the negative, "It is not possible that it will rain tomorrow." are not so common, and therefore, sound odd.
V.C.