It is not easy to be granted a visa fo the US. It takes time and money and some luck, First the applicant submits an application and around $350.00 US and waits for the interview date. This is done at the American embassy in Kingston. If the applicant has a realtive in the US it makes it a little easier. My lady friend will be trying again this spring. The first time she was turned down. Tell the interviewer you intend to visit family and be able to substanitate that the in fact live in the US.
You can also use the fiancee visa which if granted allows the person to travel to the US with the intention of marriage. The US will give you 90 days in the US but if the couple does not marry in that time the person coming from Jamaica must return home.