Were there any black passengers on board the Titanic?

Joseph Philippe Lemercier Laroche(seated right) and his family

Yes. Joseph Phillippe Lemercier Laroche was the only black man to perish in the Titanic sinking. Laroche, shown on the right in a family photo, was on board with his pregnant wife Juliette and their two young daughters
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The story of this interracial family did not become widely known until three years after the movie's release when the Chicago Museum of Science & Industry and the Titanic Historical Society featured the information as part of a Titanic exhibit.

Joseph Laroche was born in Haiti in 1889 into a powerful family — his uncle, Dessalines M. Cincinnatus Leconte, was the president of Haiti. When he was fifteen, Joseph Laroche left Haiti to study engineering in Beauvais, France. Several years later, he met Juliette Lafargue, the 22-year-old daughter of a local wine seller.

The two eventually married. Despite having an engineering degree, Joseph's skin color left him unable to find employment in France. The Laroches decided to return to Haiti and booked second-class reservations on the Titanic.

After the ship struck an iceberg, Joseph loaded his wife and children onto a lifeboat and he went down with the ship. His body was never recovered. Shortly before Christmas of that year, Juliette Laroche gave birth to their son, Joseph Laroche Jr. Juliette never remarried.