What does it look like wet? That will give you a good idea of what it will look like with new surface sealer. If it looks enough like the rest, just reseal or varnish it.
Ok. It still looks too light.
Look at the light areas with a magnifying glass, while poking at it with a knife or the corner of a chisel you don't care about. You want to play with the edge of the different colour.
If you can pick up flecks of light, showing the original colour, then your light stuff is efflorescence -- lime transported by water through the mortar or grout. You will probably find this on the grout too, but it's a better colour match so won't be as visible.
If you can scrape up flecks of dark revealing more light, then the original stone is that lighter colour and it was stained.
First case: See other answer regarding using acid to remove. Note that at low dilutions it may take a very long time. As long as you see it bubbling, it's removing stuff.
Second case: Get green and black paste or liquid form aniline dyes, and a can of compatible varnish (if the dyes are in oil use an oil based varnish, if in water or alcohol use a water based varnish. Water base will dry faster. Oil base is somewhat easier to work with.
Pick up some small water colour brushes.
Using jars like baby food jars measure out about 30 grams of varnish. Start with 1 gram of dye. (Food scale for this.) Turkey baster works well for moving small quantities of varnish from can to jar. If you measure, then you will know for next time and can make another batch that's the same.
Experiment initially on paper, until you get a green that is both lighter than the tile and greener than the tile. Suppose you find that that takes 1.5 g green dye per 30 g varnish.
For your black, start with half that.
Now, on paper see if you can reproduce the look of your tile.
You want to use a mix of colours since the tile is not a continuous colour but is made of blobs, some greener than others. Once you think you've got a handle on this, go to the Big Orange Box and buy a single tile similar to what you have. Play with painting that.
You want to build into the colour slowly -- should take 2-3 coats playing around with both colours to get a match.