Most people don't think there's much point in using carbon, unless you are using them to remove medications from the tank.
Zeolite removes ammonia, but by removing it, it can upset the cycle. Generally people view a properly cycling a tank better (and cheaper) than relying on zeolite to remove ammonia. It's also much cheaper.
If I was you I would remove the cartridges and replace them with sponge/foam or something like ceramic rings/biomax. These are good for building up beneficial bacteria.
If you do decide to keep the cartridges they do need to be replaced as they can only absorb things for a certain length of time before they get "full". I think they can also leak the nasties they absorb back into the water.
Is your filter the Stingray one? I have one of these. I managed to cram some cut up sponge into the spaces where the cartridges were.
Unfortunately I don't think your filter is strong enough for your tank and fish (if it's the one I am thinking of). Goldfish and super messy fish, so need stronger filtration than tropicals.
I seem to remember that you have a 30G tank (is that right?). If so, you should have filtrations of at least 300GPH (gallons per hour). The Elite Stingray only processes 300L per hour. So you need a lot more. You also need more media to colonise the bacteria than you currently have. I recommend getting an external filter to run alongside the one you already have. I'm not great on filtration though as I only have small tanks. Maybe someone else could help you further with filtration.
Also you might want to check out the coldwater section on the forum, there might be some topics on filtration for goldfish (do a search).
Good luck, keep up the water changes. Goldfish are super-messy, but lovely fish IMO