The best (or only?) place to buy distilled (or DI) water in Japan is in autoparts stores or Home's in their small automotive section. (Home's is kind of like Home Depot). It costs about 300 yen for a two liter bottle. The call it battery [something in kanji] with battery written in katakana on the label (the purpose is to use it in non-sealed lead-acid batteries) and the bottle is normally blue. I buy quite a lot of it for steamers and humidifiers. It might be deionized rather than distilled because the kanji is definitely not 蒸留水。Ok, it's this 精製水, which is purified water. I also recall that it's sold as deionized in Yellow Hat written with ion in katakana, but I never bought it there.

In Tokyo close to "downtown" your best bet is Autobacs in Daikanyama. Ok, I see you are in Kyoto so that's not going to help.

Another big autoparts chain is Yellow Hat.

Ok. Your best bet in Kyoto is Yellow Hat. There is one just west of Kyoto station. Type イエローハット in Google Maps.

You are definitely not going to find it in a convenience store or a supermarket. A gas station might sell it a high price for a tiny bottle. Water is "mizu" but you use the chinese reading "sui" when it is in a combo word like the above. DI water is "ionkoukansui".

p.s. There is another Yellow Hat SW of Kyoto station (3 stops away) that is near a train station. (Mukomachi).