In deep, medium-size saucepan, pour oil to depth of 1-1/2 inches. Heat over medium-high heat until oil registers 340°F to 350°F on deep-fat frying thermometer (or 1-inch bread cube dropped in oil turns brown in 45 seconds).
Place olives in bowl. Add flour; toss until evenly coated. In small bowl, beat eggs lightly. In medium-size bowl, combine crumbs, cheese, salt, pepper and cayenne.
Dip olives in egg, then crumbs. Fry 8 to 10 at a time, 1-1/2 minutes, until golden.
Olives can be fried a day ahead, then refrigerated. Reheat on baking sheet in 300°F oven for 7 minutes.