One voyage of the ship William Stetson began the 26th of April, 1855 in Liverpool, England and ended the 27th of May, 1855 in New York. One account of the voyage says:

The New York Herald of May 30, announces the arrival at that port of the William Stetson, May 27. Two births occurred on board and four deaths.

How can I find the names of the four people who died?

I tried finding the May 30th article from the New York Herald mentioned above. fultonhistory.com has archives of the New York Herald but 1855 seems to be missing May - August.

The Library of Congress lists libraries that have microfilm of the New York Herald but they're all pretty far away from where I live. And even if I were able to visit one, there's no guarantee that the article would contain the names. For example, the New-York Daily Tribune mentions the arrival of the ship William Stetson, but it doesn't even mention the two births and four deaths.

The Mormon Migration website has images of the passenger lists that the Mormons kept, but it doesn't appear to make any mention of people dying, and Mormons weren't the only ones on the ship (though they count for over 50% of the passengers).

Ancestry has the passenger list, but I also wasn't able to find an indication of any deaths. Though it's entirely possible that I just missed something.