Shops that do have scheduled afternoon dives tend to be the big boat operators based at the larger resort hotels. With them everything tends to be run on a schedule - weekly schedule of dive sites on specific days of the week, dives are a specific duration not based on your air consumption, etc. They do have 2 tank trips in the morning and afternoon as well as scheduled night dives on certain days, but, they tend to not visit some of the more advanced southern sites since it doesn't fit with their strict schedules.
In Cozumel, you will get the best diving experience if you booking with a small shop that takes 6-8 divers and runs one or two boats. They select the days sites based on the desire and ability of their divers. You'll dive your tank and computer and you'll have a long SI at a beach club. You'll depart by 8am and return after 2 dives around 1pm or a bit earlier. They don't schedule afternoon dives, but with their minimum required number of divers (check with the op to find out what that is), they will do a 2 tank twilight/night or a 1 tank night dive. With most of these ops your dives will be well over an hour each. You'll end up with as much bottom time doing a morning 2 tank trip as you would doing a 3-4 tanks with the big boat operations.
If your goal is to say you did x number of dives in 2 1/2 days, then don't stay north of town where your dive operator access is very limit and so are tanks for shore dives. You're going to spend a lot of time in a taxi or driving to meet a boat or getting to a shop for shore tanks. Stay at Hotel Cozumel, Fiesta Americana, Casa del Mar or one of the southern AI resorts and book your diving with the in-house cattle boat. They will get you out for 4 boat dives a day and you will access to tanks right at the hotel dock to cram in a shore dive. Or try Caribe Blu and Blue Angel. They are a good shop and I believe they do have afternoon trips, if you can make it back in time from the morning trip to catch it.
It's going to be hot and humid and you have a very ambitious plan. Please make time to get to Chedraui (big grocery store) when you arrive and stock up on lots of water and well balanced snacks that you can take with you during the day. In many ways, drift diving in Coz is much easier then lake and quarry diving, but don't just assume that the diving is going to be super easy for you. There are some very challenging sites with their combination of current, swim-throughs, coral formations, walls, depth, etc. 40-50 dives a year is great. I get in an avg of about 40-45. No matter where you do them or what your cert level, don't get too cocky and assume that you can jump in anywhere and immediately perform at the level of comfort and expertise you've mastered at your local dive sites that you can probably negotiate in your sleep at this point. Your buddy being a DM won't impress anyone or help you much either if he (or she) is not a Cozumel DM who is familiar with the local sites and conditions. If you get in a jam they won't know the site and/or changing conditions any better then you.
Cozumel is a great dive vacation destination. Do yourself a favor and book with a good dive operator and enjoy it. Don't get hung up on how many dives you do. Go for quality over quanitiy.
