I also think it would be fun to have what would essentially be a "reverse Morn" character, one that you would hear all the time but never see.
Of course, DS9 essentially did just that with Captain Cusak in The Sound of Her Voice
- but where her character lifted everyone up, this character would be incessantly depressed.
Basically I'm thinking that it would be the DS9 equivalent of Carlton the Doorman from Rhoda
He would be in charge of something ridiculous like Damage Control on the Defiant, and essentially be there to tell the crew that they were all gonna die horrifically whenever Sisko called for a damage report. DS9's version of Marvin the Paranoid Android.