Sending a package into Jamaica is not a straight forward project.
Sending it by USPS means it is delivered to a Jamaican Post Office which means that the receiver must go to that post office, stand in line, and maybe it will be there and maybe not. There is no home delivery and no notice of mail that is available for pick up -- at least not in the Negril area. The time quoted by the USPS is only guess work and there will be no tracking. I once used USPS with the expedited delivery you mentioned and the delivery time was actually 3 months.
There might be customs charges involved as all foreign mail goes thru Jamaican customs.
You can be sure that the package will be opened (perhaps several times) before it reaches your friend's local post office. The person(s) inspecting the package may decide they could use it 'better.'
I have used Fedex, DHL and UPS with better success as you get a tracking number. Some of those companies will process customs for you and some will deliver the package to your friend's home. Sometimes your friend must go to the Sangster customs facility in MoBay to pick the package up and pay the duty.
There is another dynamic to this process. Now your friend will know your address and perhaps your phone number. You 'might' start receiving letters/calls from your friend's family, cousins, pastor, neighbors and potentially folks your friend sold your information to.
My advice is to use Anita's advice and find a mule or wait until your next trip.
Just wanted to say that Chuck knows his stuff (as always). As good as your intent is to send someone in Jamaica something through the mail from outside of Jamaica, the downsides that Chuck explains has happened to us when we've sent correspondence and parcels to friends that live in Jamaica. Both our mailing address and email address have been sold and we know this because of mail and email we've received from people in Jamaica whom we don't know asking for money, donations, etc.
If we want to give something to our Jamaican friends, we just hold on to the item until our next trip, take it with us, and deliver it in person.