My husband has this problem because he tends to not get the sleep he should. If you can get more sleep do so, because your body obviously wants it. Don't try to AP at night. Do so in the afternoon when you're still wide awake and couldn't possibly be tired.
If he has no time to do it during the day (work etc), my husband likes to travel while reclining in a bathtub (no water in the tub) with the shower on. The only drawback to this is if you travel for a long time, your hot water could run out and you'll come back to a cold shower. But if you're doing it right, you won't notice the temperature change until you're done. =)
Otherwise he does it sitting up in a chair or on the floor. But sitting up is more difficult for a beginner. He's been doing it for a long time and can induce trance quickly.