The dye doesn't soak into dry concrete. It has to be present when the wet concrete is mixed.

Your best bet would be to try a concrete stain.

(Pedantic definition time)
Paint is opaque, so you can't see the underlying material.
Stain is semi-transparent, so you can see the underlying material.

Those definitions hold no matter what the underlying material is.

Anyway, a concrete stain would give you some color, but it wouldn't look like it was sitting on the surface. It would look like the concrete was the underlying color.

If you go this route, I'd recommend picking up a cheap concrete stepping stone and try the color on that first. Be sure to look at it in the same environment as the sidewalk, as lighting has an enormous effect on color.

Next time I'm at a hardware store I will look into those.

Thanks jeff.

The selection of concrete stains at *my* local big box stores is.. lacking, to be kind.

A contractor buddy of mine turned me on to a good local stoneyard that also happens to carry stains, dyes, and stamps. If you're not happy with the local big box store's selection, you might want to check the yellow pages.

Here is a video of an amateur that does what you need

they have concrete stains. Good colors and easy to apply. I used it on my front stoop.