If you have chosen to land with a tailwind, assess the wind: Is it steady or gusty? If you're considering landing in a gusty tailwind, I would really suggest that you rethink it. Generally you don't find gusts of less than 10kts, and landing with a 10+kt or gusty tailwind in a 172 is a bad idea. if you must land downwind with gusts, add the gust speed to your approach, so when the gust recedes momentarily on approach, it won't drop you into a stall with no warning.
If you are landing with a steady, low speed tailwind, land completly normally, knowing that you are going to touch down with noticably greater ground speed. Hold the nose wheel off as much as is safe.
Despite what is sometimes taught, I use full flaps for landing as often as I can (with one exception), unless I'm practicing flaps failed no flap landings. The more flap, the slower you're going, which is always better if you depart controlled flight. The exception is the deHavilland Twin Otter, whose full flap landing technique requires extra skill, and should not be casually undertaken.
Still, avoid downwind landings. You should always be flying high enough to be able to turn downwind for an emergency landing. And, of course, engine failure after takeoff, would not be downwind, as you just took off into the wind right?
Pilot DAR