Tyres.co.uk lists the Continental UltraContact and the BFGoodrich Advantage for the Ford Cougar in the size of 205/60 R15 91V which will fit the factory 15-inch wheels. Other factory wheel options may require different fitments, so check the tyre size, load index, and speed rating in the registration search prior to ordering.
If you open the driver's door of the Ford Cougar, you will see a tyre-size and pressure placard located on the door frame. It will show the original specifications and recommended tyre pressures, but also check the sidewall of the tyre if the wheels/tyres have been replaced.
The Ford Cougar can have differing ages on its four tyres as there are no Cougar drivetrain versions with a fully coupled all-wheel-drive system that would require matched tyres on both front and rear axles. It is also a front-wheel drive vehicle. Therefore, when replacing tyres, do so in pairs on the same axle when feasible, and when replacing tyres on one axle, the pair should be fitted to the rear axle.