Hi,
Bruce Springsteen sings this.
I had a job, I had a girl
I had something going mister in this world
I got laid off down at the lumber yard
Our love went bad, times got hard
Now I work down at the carwash
Where all it ever does is rain
Don't you feel like you're a rider on a downbound train
This use of 'downbound' is OK to me, because 'up' and 'down' are terms about your emotions. 'I feel up' means I'm happy. 'I feel down' means I'm unhappy. He's clearly unhappy in this song.
Generally speaking, it seems to me that, to sound OK, the term needs to be used in a context where you can conceive of some kind of an 'up' diection and a 'down' direction.
For example, a river has an up and a down, so I can find some references to 'downbound' ships that sound OK.
Clive