Some ryokans don't list bookings which allow only one person. Most Japanese hotel reservation systems require the number of guests to be input when searching and simply do not input solo room rates. Perhaps one could e-mail, call, or fax to inquire if they'd allow a single guest but it isn't the same as reserving online for two (or adult + reduced rate for child if allowed) and arriving as a solo guest. Booking such a reservation and showing up as one guest only at a ryokan would mean they'd have prepared food for the second non-existent guest. Mottanai and I don't think it'd start the stay on the right tone. As KI-NRT noted, most ryokans are small family run businesses, some multi generational, and I feel respecting host-guest social contracts are important in Japan. Solo availability might be different if KI-NRT called his most often visited luxury ryokan to book for a solo friend/family as such is the nature of Japanese service. Many ryokan offer slightly different inventory/pricing on Japanese vs English booking sites and I've found solo stays are often easier to find in Japanese along with upgraded dining packages.

Those which do accept one person vary in pricing strategy. Some just charge the flat per person rate you'd receive if booking for two while others increase it to cover the room fee for two but not board. Occasionally it is 100% single supplement for room and board. Some will only offer solos specific rooms which may be smaller, less desirable location, or ryokan's choice (whatever inventory wasn't sold). Solo ryokan weekday stay offerings had increased in the mid 2010's in my ryokan searches but luxury ryokans are often in high demand. It could also be seasonal as KI-NRT noted certain areas are popular for specific seasonal sights or food. Food variations such as seasonal dining packages, upgraded quality meals, or lighter meals can usually be found on JP booking sites.

Solo staying in a room which can usually fit up to four guests isn't as much of an issue for non-luxury ryokan which offer buffet or larger operations which need to fill the rooms. Some ryokan still limit those stays to lower end rooms, though. Sometimes these types of reservations are normally allocated to bus drivers (who may smoke... a lot) or tour guides. I usually book a non-smoking room if they haven't converted to all non-smoking. If the reservations don't have refurbished non-smoking rooms for solos, I specify I'd appreciate a non-smoking room or request they air out the room & provide an air purifier on the comment form. Tatami holds the smell of cigarette smoke exceedingly well.

For hotels only for natives, I've come across some of those when booking as I usually use google translated Ikyu, Jalan, Rakuten Travel, and 4hotel.jp. On the flip side, it isn't too hard to tell from reviews when a ryokan courts specific demographics of foreign guests, too, and I have my own preferences there as I feel it can influence the style of service and overall stay, especially at luxury rates. Takefue vs Gosho Gekkoju in Kurokawa are kind of an example of that. Takefue offers detail oriented Omotenashi from heated towels in all the reservable onsen, higher end dish ware in room, citrus for in-room onsen, and even hot water bottle at night. Gosho Gekkoju leaned more on architecture and design, parting snack/gift offered was less traditional, and hired (foreign) staff for foreign language ability (our dinner interactions were a combination of Mandarin and Korean, as our servers were more comfortable with those languages than English). Lower end rooms at Gosho Gekkoju are larger than Takefue's and all rooms have a rotenburo.