Look up the two or three ships that are adult only with P & O I'm not sure of their itineraries in February. Try Saga and see if they are going that way or and this would be my best bet, although they may not be totally free of children but they do not encourage their passage, is to try Azamara or if you are really flush, Oceania, Regent or Silversea. .... Neil.
Another vote for Azamara. Wonderful Caribbean itineries in Feb 09 - check out the Journey on Feb 12th.
The two P&O ships that are adult only are Arcadia and Artemis. Artemis is the smallest ship in the fleet. Arcadia is much larger and offers more amenities on board if that is something that is important to you. I suggest you go to the P&O website, pocruises.com and look at the details of each ship, as well as the itineraries. This might help. We have been to the Caribbean on Arcadia and had a fantastic time. We've not been on Artemis yet but we are going on her next year.