I have a 55 gallon with a bunch of cories. There are several other members who have them in 55 gallons too. It works out great because you can have big schools of different species they can all have there on sections of the tank.
Cories will eat flake food, frozen/freeze dried worms, brine shrimp, and sinking wafers. Personally, I feed them Hikari sinking wafers, they are not hard to miss, they have a picture of a C. Trilineatus on the front of the plastic pouch they come in. I also feed frozen bloodworm to condition them for breeding as well as live Grindal worms, and lastly they eat flake food that falls to the bottom. The main food for my cories is the Hikari sinking wafers.
Corys do well on a varied diet that has a substantial protein content.
I feed mine live blackworms, spirulina discs, Ocean Nutrition Formula One flake food, Hikari Sinking Wafers, freeze dried tubifex worms and sometimes frozen bloodworms or live tubifex worms.