I think that don'ts doesn't make much sense, because whenever pluralizing a word that shouldn't be (like a verb), there should be an apostrophe before the s, thus indicating the pluralized verb. But, I have never seen any grammatically word with two apostrophes. Plus, you need the apostrophe for don't, so dont's wouldn't be an option. I say they are both correct.
1. It is completely possible that a word could have two apostrophes
2. Don'ts would be the default "right" way of writing it if don't's can't have two apostrophes
3. BUT, when you type it on an auto-correcting text box, program, etc., Neither of them have the little squiggly red line on the bottom, which tells you if a word is spelled wrong, or doesn't exist. Try it out!