Hi lindsay and craig
Let me point out that you haven't given us enough information in this thread so that the members can respond with good and appropriate answers for you. For example, just how big is your "small" tank? What species of cory do you intend to breed and why do you only have two of them? This is not the way to be setting up for a successful effort.
What is the ambient temperature where you live? With many species of cory, unless it's winter there, or if you are constantly running the air conditioners, you won't need a heater in the tank. You will need a cycled filter in the tank while the parent group of corys are being conditioned and while they are spawning, but once you have removed them, you will not need filtration for the tiny fry for some time. It's essential to do daily water changes to remove uneaten food and freshen the water, so this will take care of any ammonia they produce. Once you are ready to add one, it can either be pre-cycled or not.
It's important to spread a little sand on the bottom of the tank. When corys spawn they might leave eggs on a clean bottom, but since they spend a lot of time sitting there, these eggs are likely to become damaged.
Another matter is that, by and large, corys are not big egg eaters. True, some breeds tend to do it, but most do not.