Yeah, I wouldn't recommend rice. Are they goldfish you have? I have fed my goldies a few things with varying success. So far I have tried-
Brocolli
Peas
Romaine lettuce
Cucumber
Corgette
Carrot
as well as their usual Gold Japan food and frozen bloodworm and the occassional bag of live daphnia.
All raw and well washed off first. Try organic if you can get it cos then you don't have to worry about pesticides. Always cut things into small pieces and give them little bits to start off, then you won't have to fish it all out if they won't eat it.
Things to avoid-
Anything fatty
meat
anything processed
basically anything that they wouldn't come across 'in the wild'
Hope that helps! If you start feeding them a varied diet you should notice the difference fairly quickly.