Hello Sarah, welcome to the forum.
Prices per Autotrader site:
2004-04 Peugeot 206 Coupé Cabriolet 2.0 16V Allure 2dr Mileage 40,000
Dealer £9,745, Private £8,395, Part Ex £8,045
2004-53 Peugeot 206 Coupé Cabriolet 2.0 16V SE 2dr Mileage 40,000
Dealer £7,775, Private £7,440, Part Ex £7,295
Beware of roof leaks, electrical problems, poor running (misfiring, cutting out), rusty exhausts (expensive). Don't spend all of your budget just on the car, keep £1000 in reserve just in case the owner is selling it because the car has faults they can't be bothered to fix (or worse, don't know how to fix).
Read through some of the problems posted on this forum to get some idea of what to expect. Then you'll know what to be looking for when you go searching for your new car. We went for a 1.6 as I got the impression that 2.0 cars suffered more problems (hydraulic tappets, exploding inlet manifolds) and are thirstier.
You're looking at the right time of year.

Come springtime, everyone will be after a convertible and prices will rise.
Best of luck,
Ron