For large, flat or convex areas you might try a dish cutter (like the MLCS 5515 or 7815 - other vendors produce similar bits).
For concave areas you can use a core box or round nose bit. Core box bits are commonly available with 1/4" to 2" diameters; and round nose bits are commonly available with 1/8" to 1" diameters.
You might find other bits useful as well. For example, Onsrud Cutter manufactures an excellent bit designed for efficiently planing flat surfaces. Your choices will depend on the shape, the workpiece material, and (necessarily) the degree of control of the router afforder by your fixture - I'd be reluctant to use a bit larger than 1" if the router was being used in any way comparable to "freehand". Safety should be the primary design consideration, since even perfect parts won't be very satisfying if their cost is measured in body parts.