You could drop the punctuation completely in the form "Bob was happy that the rain had stopped." Then I'd read it was because of the rain stopping that Bob was happy. Not simply that both were true but one not the cause of the other.

Bruno was happy; the wine was pouring. Bruno was happy because that wine was pouriung from his glass into his mouth. Sorry, that wasn't an example, just an awkward narrative.

Ok, 3 minutes left on the 2 inch thick steak under the broiler. MMMmmmm...