Preheat oven to 200 degrees F. In a large bowl, combine olives and flour; toss until olives are evenly coated. In a small bowl, beat eggs lightly. In a medium bowl, combine bread crumbs, cheese, salt, black pepper, and cayenne pepper.
In a large deep saucepan or deep-fat fryer, heat 1 1/2 inches oil to 350 degrees F. Dip each flour-coated olive into the eggs, then coat evenly with crumb mixture.
Using a slotted spoon, add olives, several at a time, to the hot oil. Fry about 1 1/2 minutes or until outsides are golden brown. Remove olives from hot oil; drain on a plate lined with paper towels. Keep olives warm in the oven while frying the remaining olives.