Not sure about pre-paid phone cards in Cozumel. Check out a travel book. I know there are international phone cards, I've just never looked into them.
There are not public pay phones aboard. You can make ship-to-shore calls from your cabin but they are expensive. It's the satellite time that gets you.
A Bad Day At Sea [with power] Always Beats A Good Day At Work
Carnival: Glory 2004, Destiny 2008, Splendor 2009, Freedom 2011, Valor 2012, Dream 2013
Celebrity: Summit 2011
Princess: Ruby 2010, 2014, Caribbean 2013, Coral 2014, Regal 2014