The only singles only cruises that I have ever heard of are through singles organizations. I don't believe that the cruise lines set these up on their own. (No reason to limit the potential number of customers.) So, I woud try googling singles clubs, then ask about cruises. Singles World used to do a lot of these, but I've been married for ages now, so am not up to date on this.
My sister uses singlescruise.com. From what I know, they have used Royal Caribbean and Carnival. Although the ships are not entirely chartered for singles, she claimed that half the ship was, so that's a lot!