Unfortunately dock workers in the C19th didn't exactly have a uniform, and largely wore the same clothes as everyone else. Although you'd expect to see things like pea coats and donkey jackets. One was more of a Navel uniform at that time and the other didn't actually exist until later.
The precursor to the donkey jacket was the good ol' woolen sack coat.
I have seen pictures of other styles that look a little more "workaday", but that was predominantly the one.
I think the guy in the fore ground is wearing a longer length sack jacket squared off at the bottom as some of them were. Obviously they tended to have a naturally grubby and distressed look. Unfortunately, getting one made would set you back a pretty penny and you probably wouldn't want to be beating it up.
On the plus side, this style of jacket last briefly came back into fashion about fifteen years ago and could be found on the high street. So looking out for mens "vintage"

four button suit jackets is one option.
Exhibit
A.
If that doesn't scream dock worker at you (which is understandable) then possibly a more
vintage style of donkey Jacket might do the trick, (and with patience you should find one cheaper than that).