You can find some places on AirBNB or Booking.com, especially in Tiraspol, but here are some options we recommend.
Finding a hotel or a hostel in Tiraspol is easy, as most of them will be on either AirBNB or Booking.com (sometimes on both sites). There are places we have tried and can recommend, with a way to contact the owner directly (and often get a better price than through the platforms).
Rybnitsa (city and region)
At the moment, there are no hotels or hostels in Rybnitsa itself. You can find some options in the villages of Stroensi or Beloci, which are about 20/25 minutes away by car. If you really need/want a room in the city of Rybnitsa itself, there is one option on AirBNB. If this option doesn't work for you, we can try to help you find an apartment.
Most local tourists prefer to rent a room or a house in the aforementioned villages. It is a great choice if you enjoy nature. If you don't have a car, taxis to and from the city are relatively affordable (about 5 euros, 6 US dollars one way).