As a matter of fact some races don't like it when others have a good diplomacy rating, the Drengin are one example, AFAIK Korath should behave the same.
You can do alot.
Decrease their military (before they declared war) by trading for their Military vessels with techs &/ influental points.
Increase your own MM by building the SCC.
Send them Freighters.
If war is inevitable, rush-buy some Medium (or bigger) hulls, research the correct on-type defense and upgrade all these hulls to 75% DEF/ 25% ATT vessels using the longest-term lease. Before ahead, get sufficient Troop Transports. Then conquer them.
The newly aquired planets usually pull you outta debt fast, even more fast if you go all-econ before-ahead, and/or have some Constructors ready to send to newly acquired Moral/Econ-resources.