Even if he had a test kit the zeolite would throw the readings off.
Ron, if I were you I'd try to replace the filter as a matter of urgency. You can probably find one second hand for not too much, either on here or on eBay, or on Aquarist Classified. Failing that, take the zeolite bit out of the filter, and replace it with sponge. Then you will provide as much surface as possible for the bacteria to adhere to, and you will not be relying on chemicals to remove the ammonia for you. If the cost puts you off, think of it this way: you're saving yourself the money you would have to spend replacing the cartridge every 4-6 weeks (and the cartridges are not cheap... how do you think these companies make their money

)
Once you've done that I would be doing daily water changes, in the region of 80-90%, to take care of ammonia and nitrite build up. You will need to do this, every day, for the next two months. It's a pain, but that's the way it is. If ammonia or nitrite build up to toxic levels, your fish will be damaged, or die. If you had a test kit you could test the levels and adjust the size of the water changes accordingly, but as you don't you must assume the levels are dangerous and do large changes, because that's better than the alternative (ie, assuming they are ok, doing little or no change and having dead/poorly fish).
While cycling you should not add more fish. Once you're cycled, normally I would say yes you can probably safely add another couple of cories. However, the stingray filters are not actually very good (hence previous comment about replacing it), so I would err on the side of caution, and keep yourself understocked rather than fully stocked, otherwise you risk the filter not being able to keep up.
Hope you find a job soon, because this hobby is very addictive, and quite expensive!