I will travel the Carnival cruise to Mexico, would I be able to do this with a green card?

I will be traveling on the Carnival cruise going from Miami, FL to Cozumel, Mexico. I am currently a U.S. resident and I have a green card as well. I have read a lot online that say you can travel with the green card to Mexico on the cruise but most of them were dated back a few years ago and I have a feeling that things may be different now. I was hoping someone can tell me if I would be fine going on the cruise to Mexico using just my green card and a valid government issued ID (driver's license). What would be the proper documentation required to travel on the cruise? I also tried contacting Carnival for information and they do not seem to have any information other than to check with immigration.