2002 Mercury Cougar Knocking in rear

This may be a simple broken exhaust mount or a problem with the suspension, best get the car to a mechanic and get it on a hoist, you can look under the car and give the exhaust a bit of a shake, it it is loose it will knock against the body and you can also feel for and movement in the shockers by hand as well.

If it sounds like someone with a hammer under your car when you go over any little bump or big bump it's your stabilizer links jack up the rear of your car crawl under its make sure there's rubber on both sides of this will sway bar links where it connects to the lower steel channel that goes from wheel to wheel most likely a piece of that rubber is missing this sounds like someone's hitting your car with a hammer

Have you had a look under the rear of the car as yet?