How many people are you allowing in the tourney?
From the tourney Help page:
In Chess.com tournaments any tournament with fewer than 8 players will only have 1 winner. Tournaments with 8 or more players will have 1st - 3rd place.
So if you have less than 8 players, you will only be able to have one custom trophy.
When I try to make a tourny it only lets me select a custom trophy picture for 1rst place. What gives?