Our now 25 month old has been on two cruises already and we have never had any problems. In fact he sleeps really well on the ship, probably because of the rocking. What we do is not tax him too much. We let him nap twice a day, we feed him on his schedule (that is whenever he is hungry) and we used the nursery quite a bit. We like to have him with us at the rotational dinner restaurants, but we remain flexible so that if he is not hungry or is tired we take him to the nursery. We also carry around some little toys and things to entertain him in his diaper bag.
FYI - The nursery is an extra charge. On our last cruise (22 months old), he loved the nursery so much he did not want to leave and kept telling us that he wanted to go "play with toys".
Our key to crusing wth an infant is to remain flexible and remember this is a new environment for them that takes some getting used to.