How did you check the alternator? Did you have it bench tested or tested in the vehicle? And if the battery is dead every morning. Then apparently the battery cant hold a sustainable charge and probably should be replaced.
It is possible that you have a draw like Beerbelly said. And he was correct in telling you how to find it. Sometimes electrical problems are a real PITA to find and repair.
'87 YJ, 4.2L built and bored, 8" of lift, 8.8 rear, AX15/NP 231J, Tom Woods drive shafts, Flat fenders, 12,000LB winch, Custom bumpers, Rattle can paint job. Never completed...