It would only be a respray if it were a) possible and b) cost effective. If the paint had been corrosive for example, and it was a very old car, a respray might not put it back to how it was and/or it would cost more than the car was worth. In which case I would be liable to buy them a new car. Now in the case of cars this is quite simple as they have a known resale value. So the new car I would have to buy them would not be brand new, just another one like the one I destroyed. And as there are handy books for such things that give a monetary value, I can just give them this in cash and tell them to go and find the car themselves.
I confess I am not an expert, but I think it's unlikely there is a similar setup for used driveways, as I don't think they're resold quite as commonly as cars... So even if you could work out the value of a 30 year old poorly maintained driveway, you couldn't buy another one for that price to replace it. If the respray does not work (or would cost more than a new tarmac drive), a new tarmac drive is what would be required.
It's actually more similar to something that doesn't maintain its value than a car, like technology; if you have a 30 year old boxy tv and I break it, it would likely cost far more to hunt down and source an exact replica than it would to just buy you a brand new flatscreen. So you'd be getting a massive upgrade at my expense. I suppose if I were super petty I could refuse to buy new and spend hours looking for a used 30 year old tv, with identical scratches and dead pixels, even if it cost vastly more than just going to Currys. So possibly op would be legally allowed to pay to hire someone to artificially age the new drive so it matches the old one. I imagine the judge would be rather bemused by the request though.
But as currently the op doesn't even seem to be sure that the staining is her fault, that would probably be the first thing to establish; right now it's like your really old tv has stopped working and I happened to be in the room. It may be my fault, it may not be. But until we establish that it is, I'm not going to be hitting eBay.