It would be "King's Heath" if the Heath is owned by just one King.
It would be "Kings' Heath" if it is owned by more than one King.
Additionally, "Kings' Heath" could refer to a singular owner if, for example, the person in question is named "Kings".
The contraction of "King is" is, as you say, always "King's". The existential contraction for more than one King would be "Kings're".
Mine's the one with the leaves and pistol in the pocket.