there is a 24 hour waiting period but not sure how far in advance you need for paperwork etc but I doubt if you do a private wedding it will take 60 days.
I have used and adore Isabelle Stewart with Weddings By Isabelle she is on facebook. I like the private option as it's usually less expensive and you can then stay wherever you like and not tied to a hotel because of their wedding package, also if you go the private route you won't have to pay for your guest to attend if they aren't guest of the AI

These are the documents needed:
Original or Certified Copies only (Certification by a Justice of the Peace (Local)
or Notary Public or Court Staff (outside of Jamaica))

Proof of citizenship - Birth Certificate, Driver's Licence or Passport (any one item).
Parents written consent if under 18 years old.
Proof of divorce (if applicable) - original Certificate of Divorce.
Certified copy of Death Certificate for Widow or Widower.