Here is a brief list of Buick Riviera's by year:
1994 - 2000 Riviera:
1989 - 1993 Riviera:
1986 - 1988 Riviera:
*** The only real difference between the 1988 and 1989 model is the back portion of the car (tail lights and rear bumper) and redesigned headlights.***
1979 - 1985 Riviera:
I'm hoping for YOU that it is the newest generation of Rivieras, because I think those are really cool looking. Plus, they could come with the supercharged 3800 engine, which will give you power and gas mileage. The interiors in the '93's - 00's are really comfy too! My mother had a 1990 and the only major problem she had was rust in the rear quarter panels. I hated working on it because the rear brake calipers were VERY testy. It required you to turn the caliper piston in, while compressing.
Another thing which was a problem area was the drivers side door. The body warped over time and the door was rubbing on the drivers side fender. You couldn't see it, unless you opened the door. Also, there was some body flex and when you went to drive, sometimes there was a noise, which was the result of this body flex, that came from the front floor boards.
At the time, I didn't have the proper tool and I wound up replacing the caliper, 2X. However, this wasn''t a big deal once I got the right tool to turn the pistons back in. This was a GREAT car and the interior was extremely comfortable. The only problem with all of these Riviera's is trying to find body / interior parts once they go bad OR if you get into an accident. I've had decent luck with eBay (had to get my mother a new rear view mirror switch, which was pretty pricey-from what I recall).
Still, if you ABSOLUTELY have to have this car, lowball the guy!!! If he takes it, and you have a laundry list of repairs, then you are only saving yourself $$$ in the long run. Save yourself some $$$ though and really look the car over. Check the pinch welds under the area of the drivers side door and look to see if there are any repairs to this area. If there are, I wouldn't touch the car unless a respectable body guy looked the car over.
The problem here is, if the car was weak and someone basically slathered some Spackle over the car and made it look pretty, the car could buckle and total itself under hard braking --OR-- during a collision. The last place you want to be is between the area where there is a weak point. I.E., sitting in a seat with your legs strewn across the floor.
The later versions of the Rivera had this problem engineered out...which is also why I'm hoping this is like a '96 or newer car.