It doesn't take a lot of scholarship to show there is no contradiction in this situation. "Christian" wasn't the original word used in either the Biblical text or on the plates in the Book of Alma. "Christian" is an English word, and neither the Bible nor the Book of Mormon was originally written in English.
Even if both sources had used the very same word, the fact that Luke wrote that the word "Christian" was first used in Antioch would be proof of nothing. He had no knowledge that a prophet in the New World had used a similar term to label the followers of Christ one hundred years earlier.
The word "Christians" is the word Joseph Smith chose to use while translating Alma 46:13-15. Apparently it was the word in his vocabulary that came closest to the word originally used on the plates.