There is only one genuine alternative to chlorine: PHMB, (polyhexamethylene biguanide), sold as Baquacil, Softswim, Revacil, etc. You can look in this forum section for info: http://www.poolforum.com/pf2/forumdisplay.php?137
With a tiny, frequently used small pool, one of the most important things you can do is frequently replace your pool water. Trying to manage a pool with a poor gallons to swimmer ratio is difficult at best. Most people in the pool industry will not use a commercial spa (spas have the WORST gallons to bathers ratio).
The problem is, that the chemicals that oxidize (burn up) the people goo (urine, sweat, lotion, shed skin, skin oils, etc.) have a hard time keeping up when as the ratio of gallons to bathers decreases.
I will caution you that most 'non-chlorine' systems are EITHER actually dependent on chlorine or bromine OR are unsafe. PHMB systems are the ONLY systems recognized by the EPA as a true non-chlorine pool sanitizing system. But, PHMB is not recommended for spas. I'm not sure what they'd say about a 1,000 gallon pool. Personally, I wouldn't let my own children in a 1,000 gallon pool using PHMB, if other children or adults had used it -- the risk of disease would be too high.
Please keep in mind that the EPA sanitation test does NOT test for efficacy against viruses or amoeba, and PHMB's efficacy against those pathogens is a small fraction of chlorine's efficacy. Of course, the other 'non-chlorine' systems are even worse.
I don't know that I can help you more than that. We don't support PHMB use here, and you don't want to use chlorine.
You may, if you wish, look that the "Super Simple recipe" for Intex pools; there's a lot of info on that page relevant to Intex pool operation. There's a link to that page in my signature block.
If you want to know more about chlorine and asthma, there's an extensive recent discussion of that topic in this thread:
http://www.poolforum.com/pf2/showthread.php?21911
Good luck.
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