Slimz

First things first, you child's father would have to give permission for him to leave Jamaica, even if it is for a visit. So without the father's consent he will not be granted a visitor visa.
 
if the father consents, then he would be able to visit you if approved. 
 
We are not sure of his chances of approval though. You are a strong tie to the US which may be a red flag.
 
Also, you want him to get the visit just to visit, correct?