If you are on Carnival, they use the international pier. Dive With Martin is by far the most convenient. We chartered our own boat for $400 us for 4 divers so we didn't have to worry about meeting a set departure time. It takes FOREVER to get off the cruiseship. DWM is about a block walk from the pier. Once we got there, we were on the boat within 10 minutes and had 2 great dives with plenty of time for shopping afterwards.
STAY AWAY FROM THE CATTLE BOATS that pack 20 divers on a boat. They cater to cruisers. I don't know if Sandollar is still the company that books the cruise sponsored trips, but I have heard horror stories about them. Several other dive operators will have later departures for cruisers, just make sure your on a boat with no more than 6 divers. Aldora, Blue XTSea, Blue Magic, Tres Pelicanos, and Living Underwater are some operators frequently mentioned on these boards. I have dove with Aldora and Blue Magic as well before and both are great.
If your ship comes to the downtown pier, (Disney?)it opens up lots of operators that are based downtown. You can always catch a cab to your operator. Vans are available for a group. One possibility might be Aldora who spends their surface interval at a beach club. The non-divers may be able to take a cab to the club and do the beach thing while the divers do their thing. Blue Magic spends their surface interval at a beach with no improvements, but I think it is prettier.
DWM did our surface interval on the boat. Keep in mind if you have at least 4 divers, you can probably get your own boat and anything is possible, it just depends on what you want to pay.
Email several of the dive operators and see what they suggest. Cozumel is quite possibly the friendliest place I have ever been in Mexico, Every operator I have ever used was genuinely concerned about us having a great time. Tell them what you need and I'm sure they will work to accommodate you.
safe travels and Merry Christmas!
jay