You can rent a house pretty much anywhere - it`s more common than you might think. I know a handful of people who own older houses that they started renting out when they built a new house. The buildings tend to be old and run down and renting is usually very long term so they don`t appear as much on the market as apartments - but they`re out there.
In my personal opinion, you`re usually better off renting an apartment in the long run because they tend to be better kept and aren`t nearly as expensive, as houses tend to be 1.5 times the normal price of the area for the exact same amount of space.
Unfortunately I can`t offer any specific help for Kyoto, but have you tried the regular Japanese rental sites? Those catering to foreigners tend to be over priced with tons of mark ups (over the already present normal fees).
Apaman Shop comes up with 36 houses in Kyoto city.
Able comes up with 62 (including terrace houses).
Home's has over 1000 listings, though some are closer to shed than house...