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According to this link, Marco Polo has 24 hr self-service tea/coffee - but it's outside !! Well, she is an older ship. Hopefully she doesn't have outside toilets too LOL
http://www.cruisecritic.co.uk/reviews/review.cfm?ShipID=48&pgtype=dining
So take a thermos, on most ships you can get hot water from the buffet 24/7. And mebbe take some UHT milk jiggers in case the ship provides only in large jugs.
Chris