Matt, finding singles on a non singles cruise is hard. However there are usually more women who might be single then men.
Do ask the maitre D to seat you with other singles during dinner, and ask the front desk on the ship when the singles meet and greet is, make sure to attend this. Also talk to as many people as possible and let them know your single see if they know any other singles.
Next cruise book a singles cruise, with a singles agency see Ann Cambells singles calender 2006 on this website for a complete listing of singles agencys.
Carnival Mardi Gras 1987 (Bahamas)
Carnival Legend 2005 (Exotic Western Caribbean)
Costa Mediterrenia 2005 (Eastern Caribbean)
Carnival Pride October 2006 (Mexican Rivera)
Carnival Legend 2007 (Western Caribbean)
Carnival Glory 2009 Western Caribbean
Carnival Liberty 2011 Eastern Caribbean
Norwegian Spirit 2011 Western Caribbean Carnival Miracle 2012 Southern Caribbean
It is preferable if traveling solo to go on an organized singles group since there are so many families cruising together these days, blocking rooms for grandma, grandpa, aunts, uncles, cousins, etc., with no room for outsiders. Then you have your couples but few people by themselves. With an organized singles group you can always find some activity, someone to hang out with, dine with, etc.
Check my singles calendar in the singles section for an up-to-date list of singles cruises now available. And remember, if you are going Halloween or New Year's--the most popular singles cruises of the years, book asap.