If you don't have a fridge, the cabin steward can keep your ice bucket filled, just let him/ her know you need that. You can grab an extra milk carton or two at breakfast and keep them on ice in your room. Then replenish your supply by getting extra cartons at each meal. You can also get more from toom service, but it takes awhile (30-45 minutes) to come, so plan ahead and on some lines you need to have cash to tip the person who brings your order (RCI) but I think on carnival they bring tabs with 0 balance and you can charge the tip. Also I'd keep some apple juice to appease your child if you're waiting for milk, I always watered the juice down for mine. Then give the milk when you have it.