It's possible. Do the tramway when you return. It's across the street from where most of the ships dock. Magen's is about a 20 minute ride away. What ship are you on, some dock in Crown Bay, which would change things.
Ronnie

Thanks, I will be on the Royal Caribbean Explorer of the Seas, hope that doesn't change anything.

Hi Rob,
Looks like according to the cruise ship schedule that you will be in St Thomas on Wednesday with a lot of other ships. Its going to be crowded that day so from our experience(three different cruises to St Thomas port) i think you should get off the ship asap(if you are going to have to tender in then get your tender ticket quick). Be on the ball or it will be awhile getting off since the Explorer carries many passengers. Believe me, the extra hustle to get off will be worth every extra minute you get to stay in St Thomas. You are in for a treat!!! It looks as though you will not be a Crown Bay so you can catch a rental car right off the ship. The car rental place is right across the street from Havensight. If those are all gone, catch a cab to the next closest car rental co. Maybe leave the wife and two kids behind and pick them up at a specified time so you can move quicker to get a car at that location before those other cruise passengers beat you there. Once in your rental car, just take off. Great drive and catch some beaches on the way. Get a map from rental car co. Magens is BEAUTIFUL but so is everything else. The rental car is worth every penny and it gets you away from the crowded main area. Lots of Luck on your cruise and I hope you get this before you leave. Happy Cruising!!
Beth In Atlanta

p.s. remember to give yourself plenty of time to get back into crowded Havensight area to return the car and be back on the ship in time. 3-5 pm very crowded streets in that area especially with that many cruise ships.

My husband and I - 2 slightly hyperactive adults, no kids - did this in April, 2001 from the Grand Princess.
We went across the street from the docks to the tramway entrance, and to Paradise Point, where we stayed about half an hour or so. We went back down the tramway, took a taxi to Magan's Bay.I think we got there about 10 or 11. We arranged for the same driver to pick us up about 2 pm and take us to the downtown area. We headed back to the ship by taxi over an hour early, we thought, but it turns out we just made it with a little time to spare, due to the traffic..

Magan's Bay is wonderful, with shade trees available right on the beach (in April) until almost 2, white beach, and pina coladas delivered on the beach. We rented a locker, a float, and snorkeling gear at the concession on the beach. (I'm sorry, I can't remember the prices.)