Repairin rotten joists
The quickest easiest way I can think of, would to be sister the old joist with a new one. Ideally the new one should be the length of the span but 3/4 of the span should be solid. Just don't splice in at the end. It needs to be fastened together for a substantial length for strength. Fasten the two together with many steel screws Decking type (not drywall as they can be brittle) about 2 or 3 about liner foot and a construction adhesive would also help.