Rinse livers; drain on paper towels.
Coat evenly with mixture of flour, salt, pepper, and cayenne; set aside.
Wash apples; remove cores.
Cut into 1/2 inch slices, to form rings.
Heat 2 tablespoons oil in frypan over medium heat.
Add apples; cook until lightly brown.
Turn slices carefully; sprinkle with sugar.
Cook, uncovered, over low heat until tender.
Remove from pan; reserve.
Heat remaining oil over low heat.
Add livers and onion rings.
Cook over medium heat; turn often to brown all sides.
Transfer to warm serving platter.