Jamaicans speak English, so they say "I love you" the same as people living in any other English-speaking country. The accent of Jamaica, however, is famous for sounding unlike anywhere else.
Jamaicans speak a language called Jamaican Patois, which is an English-based Creole language created by slaves in the 18th century. These slaves had direct exposure to English speakers from many different areas of the world. The terminology and slang used by slaves throughout Jamaica and the surrounding islands has morphed into new words and been modified. Despite all of this, the only way to truly say, "I love you" in Jamaica is to say those exact words.