If the reason you don't want to go back to using bleach (or chlorinating liquid) for a chlorine pool is that frequent addition is inconvenient, you can consider several automated options. One is a saltwater chlorine generator (SWG), another is a peristaltic pump, another is The Liquidator (though some find issues with it while for others it works out OK). Even with manual dosing, if you have a pool cover you can often just add chlorine twice a week (that's what I do with my pool). Without a pool cover, you may need to add it every day or two.
Other alternatives, that are more expensive, include using Trichlor pucks/tabs along with a weekly algaecide such as PolyQuat 60 and periodic dilution of the water.
It's unfortunate that there isn't a concentrated source of chlorine that is inexpensive, slow-dissolving, and does not contribute to Cyanuric Acid (CYA) or Calcium Hardness (CH), but that's the way it is. The SWG is the closest you get to convenience since the chlorine is essentially made "on-site".
Richard