Some more general suggestions:

Several eateries at pontocho keep their own gardens and offer the guest a guided tour before dinner. It might also be worthwhile to contact some of the tea ceremony schools in Kyoto as they have their own tea pavillions f.ex. in Gion that include traditional gardens. It's always a nice part of the tea ceremony when the slide doors are swung open revealing the garden behind. And last but not least, many Kyotoites living in traditional houses actually use a professional gardener to maintain their house gardens. There should be homestay programs available through the JNTO or other organizations or maybe you have your own personal contacts in Kyoto.