Perhaps dog lovers could charter a ship on its last cruise before a major overhaul or retirement.
The cruise line wouldn't be as worried about any damage that the dogs would do and passengers would be aware that they have to watch for surprises as they walk the deck.
February 1998 - HAL Westerdam E. Caribbean
January 2000 - Carnival Ecstasy - Mexican Riviera
February 2002 - Costa Atlantica - W. Caribbean
February 2004 - Grand Princess - W. Caribbean
March 2007 - RCI Voyager of the Seas - E. Caribbean
May 2007 - RCI Voyager of the Seas - Western Mediterranean (Mrs. E. & daughter only - I had a medical emergency)
October 2007 - RCI Adventure of the Seas - Southern Caribbean