score:9
First, if it's cheap, it's not a ryokan. You're welcome to dispute that, and some of the other answers to that question do (mostly by redefining what "ryokan" means), but I'm sticking to my view. Kyoto is particularly bad for "fake ryokan", because there are lots of people who want to stay in one without the pricetag, and that's how you end up with things like the "capsule ryokan" (which is at least mildly interesting)
So my recommendation to get a ryokan-like experience without a ryokan-like price is to stay at a temple: you get to sleep on tatami, bathe in an ofuro, enjoy a classic Japanese dinner and breakfast (vegetarian, which is why they're cheaper), and as a cherry on top you can (and should) attend the morning service if you want to. There are lots in and around Kyoto, and this site lists quite a few. Mount Koya is particularly good for this, although it's a bit of a hike from Kyoto.