How to repair botched, colored concrete?
I'm not a concrete expert, but if you don't mind a little extra height (which is often good for aesthetic and drainage reasons,anyway) you might try:


Sandblast the crud off of the top layer of the slab. You want to leave the surface roughened too, and sandblasting accomplishes both.
Was the old slab reinforced with mesh or rebar?  If not, then maybe lay some reinforcing mesh down now.  If it was me, I'd use concrete screws to fasten it, every couple of feet.
Saturate the old concrete with water, so it doesn't "rob" the new concrete while it's curing.
Pour at least an inch of "topping" or small-aggregate concrete.
Finish to taste.


It's probably best to test everything on one slab first, to see how it goes.
See this article for another take on it.



If you do mind the extra height, sandblast and wet, but just use a thin layer of proper topping or finishing cement.  Don't be surprised if it doesn't hold-up as well, though.



Just about any hardware store carries "Topping" cement.  A very common product is QUIKRETE® Topping Mix. Note that it requires an additional "Acrylic Fortifier" if you use it only in a thin layer.

For an even thinner overlay, there are "skim coat" products like "SonoSkim Concrete Surface Finishing".  I've never seen one of these hold up in high traffic areas, but you can reapply it as needed.