NCL is probably the best option. Freestyle Dining, No set times, No set table, just like going to a land based restaurant. Also NCL is in the mid price range. Good Luck & talk to an Agent who knows cruising & can advise to your requirements.
I would try either Thomson, Island or Ocean Village cruises they are very casual in their approach to cruising.
NCL, or if you have a larger budget Azamara or Seabour.
Princess Cruises do both. One restaurant is used for set times and one for anytime dining. You choose which you prefer when making your booking.
P&O do freedom dining. This allows you to turn up at selected restaurants when you choose and available on Oceana and Ventura.
Try island cruises great company cant do enough for you nothing to much trouble for them if you want to eat bye your 2selfes they will get you table for 2 or you can eat in 24/7 beachcombe.