If you have an all day stop and are willing to pay extra for a private Instructor it might be possible within the constraints in one port. None of the cruise packaged dives will be more than 2 dives at a location so you'll have to arrange it yourself. IDK if an instructor will be willing to do two dives then pass you on to the next location for two more but I doubt it.
Assuming you can set it up outside the cruise line parameters - Belize is probably out as they tender you off the ship moored offshore - even the dive operators pick you up there - so not enough time.
It might work in Grand Cayman. Don Fosters is the cruise operator - they're about 1/8 of a mile from the cruise dock - you're tendered in there also. They're a bigger operation so
possibly have an Instructor available that could work with you. Cheeseburger Reef is their on-site shoredive - probably where they do their non-cruise certifications. From their website:
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usually might be able to be modified if you're willing to pay extra for private referral dives. You will be anyway as no one is going to do O/W referral dives for the price of a cruise package dive.
Welcome to Don Foster's Dive Cayman Come Dive with Us
Another option there might be Eden Rock. It's about 100 yds. south of the Cruise port also - a shallow shore dive location so it might be possible to arrange 4 dives and still make your sailing time. You'll see your ship straight out from there the whole time.
Cayman's Best Boat and Shore Diving
Some ships seemed to sail around 5PM - maybe find out who has the earliest arrival and latest departure. I just glanced at the schedule for next month - Carnival Liberty is in port from 5AM to 5PM. IDK if it's a Miami origin though. I don't cruise but I have read that in the tender ports it's a good idea to get in line early to get off the ship. We easily do 4 dives per day shore diving on Cayman - usually done by early afternoon - so I don't see why that couldn't work for you. Most Cayman operators are staffed to do 2 afternoon dives usually also. You can check here for your planned dates:
Ship Schedules
On Roatan the cruise operator is Anthony's Key. They're on the north side, the cruise port is south. It's a 45min. shuttle ride each way so that probably doesn't work. Plus they only have 1 shuttle run and leave time to
explore their gift shop.
Try contacting Barefoot Divers - they're about a 10-15min. cab ride from either cruise dock (Mahogany Bay or Coxen Hole) I mention them because they work with cruise schedules, are a small boutique operation and with advanced notice could possibly arrange for you to do all four dives in one day. They have several boats and Instructors and normally would be only diving with people from the resort - not everyone that stays there dives. We did two dives with them one morning and were their only business.
They also have
three 2-tank trips per day so there might be more flexibility in working within your time frame. Some start at 35' or so and go deeper so it could be possible for you to do shallower check-out dives without impacting any other divers. I don't think there's a shore dive off the resort - it's behind a breakwater and too shallow. They're also a PADI IDC so have the staff available to work with you. Also we found them to be extraordinarily accommodating.
day dive packages|cruise shippers|full valet service
I think if you can make it work, Cayman is your best option though. Since there's shore diving nearby the Instructor doesn't have to deal with your first dive being off a boat.
good luck,