Is there anyplace on the Island that I could rent a couple of rod and reels ? I am also not opposed to buying them, depending on how much it would cost me and then just giving them to somebody there when I leave.

stop by the fly shop and ask. Often resorts will have one tucked away. Fishing from a dock with just a line and hook also works. I just gave my fish to the Maya groundskeeper for the resort fishing next to me. http://www.captainsharksbelize.com/product-category/fishing-equipment/

Captain Sharks, behind the airport, usually has some reasonable rod and reel combos that you can buy and then give away. I've done this several times as fishing gear doesn't keep well if not used regularly

or use the link to captain sharks I provided. When you are done saltwater fishing soak the reel overnight in fresh water overnight. Have it back shopped once a year.

Captain shark is a good place. It's cheap.