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There really are no good alternatives.
Bromine is good, but can't be stabilized against sunlight, so it isn't ideal in an outdoor pool.
Biguanide works well at first, but it is expensive and a lot of people start having problems with it after around three years.
The copper/silver/ion systems aren't real sanitizers. They are primarily algaecides that keep the water looking nice, but their activity against viruses and bacteria is too slow for pool safety.
Stick with chlorine, whether in a feeder, by adding bleach or a SWCG. It works and is about as inexpensive as any method of sanitation.