Agreed, the filling is not so difficult, the dificult bit will be getting a seamless match. Whilst not cheap you could try MagicMan or see if there's an independent surface repairer in your area.
You can use Stonefill mixed with acrylic artist paints. It is a "clear"(ish) 2 pack filler. Unfortunately, even if you mix it to a sympathetic colour it will be uniform in colour and may stick out like a sore thumb. You will also need to sand it flat and then polish the surrounding areas.
As per @freddiemercurystwin 's post, MagicMan/etc will probably do a better job than you can, but you will pay far more than trying it yourself.
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