how to keep chlorine in pool with broken pump?

You can put tablets in a floater but the same rules apply, It needs to be circulated. You can put bleach in the pool and use the brush to stir it up or you could use a sump pump to promote circulation in either case.
 
Generally speaking, you can walk around the perimeter of the pool and dribble/pour bleach into the pool as you go around. It distributes the bleach around the pool and allows it to disperse more evenly than just pouring it in one spot.
 
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