そのうわさは本当であったはずがない　
そのうわさは本当であったはずがなかった
そのうわさは本当であるはずがなかった

Do these make sense? Is there any difference?

Vedi una traduzione

They do make sense, but the first two sentences sound quite unusual because of their meaning:

そのうわさは本当であったはずがない。
It's not possible that the rumour WAS true.
(> So now the rumour has become true???? I can't imagine in which situation one would say such a sentence.)

そのうわさは本当であったはずがなかった。
It WAS not possible that the rumour HAD BEEN true.
(> The relation of the time is too complicated to understand in Japanese. No one would really make this kind of sentence even if it's really the case.)

そのうわさは本当であるはずがなかった。
It was not possible that the rumour was true.
(> It's just that the speaker is telling the situation in the past. The sentence sounds normal.)