Carnival offers tours to Altun Ha and Xunantunich, but not Lamani. It is a fair distance to go and the amount of time in port is not quite long enough to accommodate a tour so long. It takes a while to get there and a single breakdown or problem could mean you miss the ship, if booked on your own, or the ship has to wait for you and you have literally no time to do anything else but run from the bus to a tender.
Belize has incredible Mayan ruins and it might be best served to go do a land vacation that would permit a 12 hour day to visit Lamanai or Xunantunich. I LOVE Belize and would go back there again!
2007 Victory & Triumph
2008 Conquest & Liberty
2009 Valor, Freedom, and Splendor
2010 Glory and Liberty
I did this tour in 1999 when I sailed with Premier Cruise Lines aboard the Island Breeze. We went on a bus, then a high speed boat up the river, the to the ruins. Was worth it, but it was booked through the cruise... It's worth seeing!
It is a long tour so don't expect to have a bunch of time at the end to shop at the port. We picked up a few tshirts right at the ruins site and locally made jewelry. Our guide was really entertaining...can't for the life of me remember his name..very different, sorry