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A superconducting coil-dominated magnet was designed for a fixed-field alternating gradient (FFAG) accelerator for carbon cancer therapy. The magnet consists of deformed pancake coils with negative bends and a saddle-shape coil with negative bends wound with coated conductors. The minimum flat-wise bending radius and the maximum edge-wise bending strain were considered when designing the coils. The field error was evaluated by using the integrated magnetic field along the beam direction and the local k + 1 value to optimize the shapes of the coils.