I don't think that there's any alternative to using yeast, but someone correct me if I'm wrong.
The little amount of yeast in the bottom of a bottle is an essential part of home-made beer, and as far as I see it you've got two choices. The first is just to be really careful when pouring the beer from the bottle to the glass so that you don't get any yeast in the glass. Be sure to store the bottles upright so that the yeast stays in the bottom.
The other way would require a bit more equipment but will give you a yeast-free beer: First let the beer ferment completely in the plastic container you use. Leave it into the container for about a week or until its completely clear (the yeast will sink to the bottom of the container). Siphon the beer into another container and be sure that no yeast comes with the beer. Bottle the beer and carbonate it artificially (for example with a soda machine).
You might also want to check out the Cooper's website (
www.coopers.com.au), there are some tips about beer making.