Does he have to lay down on his bed? There are plenty of places in the public areas he can sit and relax. He could also go sit on a lounge on the pool deck although that may be uncomfortably warm.
The cabins are not normally open until 1:30 as they are still cleaning and changing over the rooms from the last cruise. But you can get on the ship much earlier. The rest of the ship is open for use - Lido deck buffet area, the promenade deck which has many large soft chairs and couches and several bar areas for him to sit.
If he has to be able to lay down, then as Dave suggested, plan to show up about 1PM or 1:30. STILL go to the VIP check-in area and let them know about his handicap and they should assist you with priority boarding. If you can't find he VIP area, just ask any of the terminal personal and they should be able to help.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007