Depending on weather, probably 8 or 9 am also depending on when they dock...
I think Cozumel lands you right at the dock, so there are no tenders...I forget about Ocho Rios...
The other 2 are tenders...
2010--RCCL Independence of the Seas
2009--RCCL Freedom of the Seas
2007--RCCL Liberty of the Seas
2005--RCCL Brilliance of the Seas
2002--RCCL Monarch of the Seas
2001--RCCL Majesty of the Seas
1998--RCCL Majesty of the Seas
1996--RCCL Majesty of the Seas
I'm going on Liberty to Labadee, Ochos Rios, Grand Cayman and Cozumel in March.
The ships dock in Labadee, Ocho Rios, and Cozumel. The only tender port is Grand Cayman. When the first tenders leave depends on when you arrive and when the ship is cleared by local authorities. Bear in mind that you will need to get tender tickets (free) for the first several tenders. When these are handed out will be announced in your daily Cruise Compass. Space can be limited on the first tenders because they offload passengers who bought tours from the cruise line during this time and that can eat up lots of space.