It's a widespread fallacy that the only way to chill a whole house is with central air conditioning. While in some cases this might be true, ductless mini-split systems should also be taken into account.
Even if a strong system is required, especially in a big house, a ductless mini split is capable of doing the job. It is capable of chilling a full house, from the foundation right up to the attic, with the proper size system in place.