What United States coin does not have the word god on it?

You are probably thinking of the errors that occurred on a small fraction of the new Presidential dollar coins. The mottoes, date, and mint mark are all on the coins' edge, a technique called edge lettering.

The mint has not used edge lettering for almost 2 centuries and workers were not accustomed to sending coins through a second press that adds the lettering. A couple of boxes of coins were forgotten, so they don't have dates, mint marks, E Pluribus Unum, or In God We Trust on their edges.

Unfortunately a few extreme right-wing religious zealots out there somehow decided that this goof was part of some great conspiracy to remove the Word "God" from our coins, and have been beating drums about it ever since.

Well, the coins are also date-less, mint-mark-less, and E Pluribus Unum-less as well as being "god-less".

Purely and simply, it was a case of human error. Nothing more, nothing less.