Original answer to original question:
Assuming that he has made a high "ask," you can counter with a "lowball" bid, by offering about half of what he asked. If he asks 100 and you bid 50-60, you might split the difference at 75-80.
This is "standard" bargaining advice. But before you take it, check the "blue book" value of a car of similar make, age, and condition online. It's possible that even 50 is too high a bid, and it's also possible that he's asking 100 for a car worth 90, in which case 75-80 would be a more reasonable bid than 50-60.
Here is a new response based on the edited question:
The ask is at $4700. A bid of about $3800 is not unreasonable (about 80% of the ask). If you're lucky, you'll be able to split the difference around $4200. If it's $4250, you may have decide whether or not to "stretch" for $50.
If the seller insists on more than $4200, be up front. Say, "I only have $4200. If you want more, you'll need a new customer." Faced with this choice, he may come down. He may not.
Another possibility worth considering (for some people) is to offer $4000 down, and the balance of $700 at $100 a month over, say, seven months. (Save the extra $200 to give yourself a cushion.) He gets his price. You get "soft" terms (extra time to pay).
