How many seconds of following distance should you use if it's raining and you are tired while driving?

Usually in good conditions you want to have 2-3 seconds of distance between you and the car in front of you, for every hindrance (ie. rain) you add one second of distance. So in your case being both tired and having to deal with rain, i would say have at least 5+ seconds distance. I wouldn't recommend driving while sleepy as your reaction time and judgment decreases while tired, if you think you are getting too tired please pull over and take a quick nap.