On Roatan - afaik the Carnival dive operator is
Anthony's Key Resort. Since they're on the north side they shuttle you from the port.
Carnival Valor docks at Mahogany Bay - the new Carnival cruise port so a closer option would be Barefoot Divers - they're 5mins. (by cab) away and have a
cruise program. AKR is a good option if you or any non-divers want to interact with the
Dolphins.
I've dove with AKR and Barefoot Divers and have no problem recommending either.
Since most dive sites at either location are only about 10-15 mins. away you may have time post-dive for sightseeing/lunch - it's 1/2 mile (or less) from Barefoot Cay to French Harbour, one of the small towns on the south side. You could probably walk there from Barefoot. AKR is in it's own compound and there's not much nearby.
+1 for donhealy's recommendation on GC. Off the Wall, Wall to Wall, Neptune's, Ambassador Divers are often recommended here. The first two book out of the Lobster Pot dive center in Georgetown. With all your fellow cruisers in town (and the likely 2-3 other ships) Georgetown will be somewhat of a mess so plan accordingly.
Note that you're tendered in there also except that your ship will be in the harbor or just outside it - depending on when you arrive. The
cruise operator on GC is Don Fosters - I've no personal experience with them but the amount of divers per boat/size of their boats puts me off. All the diveops I listed above are 6-8pax maximum. You may not be able to get to Neptune's/Ambassador in time for the morning 2-tank though - depends when you arrive.
Links to all the diveops:
Cayman Islands - Grand Cayman, Diving