How to correctly express the subjunctive mood in future tense?

Solution 1:

"Were to" seems most fitting.

In your options, the first one is wrong (singular subject "sun" needs an s on rises).

The second one doesn't express the subjunctive mood like you're looking for; "rises" is more indicative.

The third of those options gets at the subjunctive mood, but isn't specific to the future tense.

The fourth is the best of what you've listed.

You might also consider:

5: If [only] the sun would rise in the west, ...

which has more of a wistful sense about something you don't expect to happen but really wish it would. That doesn't fit your "then I would give you ten dollars" very well.