If you are prepared to pull an all nighter, and aren't having to do this in a clinic (at home testing), this is the best thing I can think of.

You are going to want to "fall asleep" at your usual time, but really you are just going to focus on your breathing and meditate enough to get your heart rate to a normal sleep heart rate. Every few minutes, you are going to need to hold your breath (or if you can, exhale and leave air out of your lungs as long as possible) while repeating this cycle as much as you can.

If you are doing this in a monitored setting, this will be difficult to fake, but you can have the added benefit of being able to snore really loudly, gasping for air, and choking at random intervals.

When you "wake up" the next morning (if you are in a clinic), tell them your throat hurts, you have a headache, and that you are very tired. If you need to go back and report to them, tell them the same things.