Just wanted to give you all an update on this.
It turns out that you can only be married by a priest in a church.
There is one catholic church on the island - I believe it's called San Pedro Catholic Church.
There is no resident priest on the island. I found this out after calling the Holy Redeemer Church in Belize City and speaking to Father Lazarus Augustin (sp?). According to Father Lazarus, there is a priest that flies in weekly from Belize City to say mass on Sundays. He is also the person that generally performs weddings. His name is Father Carl Heumann. I have his contact information if anyone needs it.
In terms of requirements for geting married in a Catholic church, I confirmed this with both priests. The only type of information they require is baptismal certificates issued within six months of your wedding date (cannot be older than that), a letter from your local priest or parish indicating that you have gone through marriage prep, and all other marriage papers that your local parish is preparing on your behalf. Confirmation is highly desirable, but NOT NECESSARY.
Many people have told me that the church requires confirmation and first communion papers, but this is not the case.
Anyway, I thought this might be helpful to couples interested in having a catholic wedding.