No established system available, nothing that would get there faster than 7 days or so, even then. Acts of God are possible with buckets of money and most importantly knowing someone who is on the next Southbound flight.
You have the item shipped to your new-found friend and courier/mule in the US. They examine it and determine its not a criminal item. They drag it to Roatan.
Let's say their luggage actually does arrive.
Then they have to hand the item off to an intermediary because they are not likely going anywhere near TBR. How it gets to you then could have several paths. That could be the most problematic point.
There are common carrier options to the Mainland, you can even do overnight-ish packets to Tegucigalpa (if you have cubic metric Oprah money), but then that transition past a 24 hour shipment over to Roatan will likely cost another 12 hours to get the local island courier to drag it even next door- which they aren't.
So, FedEx or some such, if you want to throw down the lottery money to accomplish that? Will likely take 72+ hours for an "overnight flat pack". If it won't fit in a flat pack, it might cost Dubai money.
How's a "DIR Practicioner" doing over there at TBR? They lookin' atcha kind if funny, or just not notice? Don't you guys carry three of everything?
Hope it works out ok for you.