You didn't say whether they were black spots or white spots. The Ilfochrome spotting dye set is the only thing you can use on that surface. Whites spots are really quite easy to remove.
What I do is use a small, plastic, watercolor pallette with little dimple wells around the perimeter. I use a large brush, wet a spotting color and put some of the dye into the well. Clean the brush and do that for each color. Let the dyes dry in the well so they're solid again. Use a small spotting brush, wet the brush, pick up the colors you need and mix them on the flat pallette area. Mix them slightly lighter than you think the color really needs to be. Spot the area with a light stipple pattern just like you would with a black and white print.
I like to use distilled water for the dyes as it will not leave a residue on the surface. You have to make sure you don't get the area too wet or you'll leave a ring around the area you're spotting - try to be as "dry" as possible.
Now for black spots - a real, royal pain. They have to be bleached out and then spotted back in. This is really difficult because the bleach has to sit on the surface long enough to remove all of the dye making up the black spot. Invariably, what happens is the bleach spreads very slightly as the emulsion swells - and you end up with a bigger white area that needs to be spotted.
If this is a large area or lots of spots, reprinting is far, far faster.