You might try Oxalic acid first. It is less agressive and less costly. I have used it successfully to remove black marks from my deck. It is available at paint and hardware stores.

Maple often has black mineral streaks within it. This is just a natural part of the tree growing. Im not sure if this is what you have or not, but it is a possibility.

Hi,
These may be rust stains from the nail heads. All of my window sills (1900, pine) have them. Rust stains are really impossible to remove perfectly. If it has to be perfect, you could drill them out with a 3/8" bit, and make matching plugs and glue them in. Not dowels, but face-grain plugs made with a "plug cutter" in a drill. When the grain is selected and matched carefully, and they are sanded flush and finished, plugs are a craftsmanlike way of dealing with a bad situation.
Casey

The black stains aren't from nails or streaks in the maple. The whole sill in one room is darkened, as are the lower window jambs. Will test out oxalic acid. I do have extra trim left over from a neighbor's renovation, and I might just cut new sills, as a last resort.