Well thanks to TLR's notes, Albacore-Class cutters generally have no more than 25 officers, so I just worked out what departments had what officers (Tactical only has one, seeing as how its department chief is just an ensign less than a year out of the Academy).
I'm not entirely sure how Warrant Officers fit into rank structures, so I leave them out. As for how many of what rank, I just went through the departments and allocated ranks that seemed appropriate.
For example: Engineering has one officer (minimum) to oversee the each watch, the warp systems specialist is always in engineering (monitoring the core and other related systems), the diagnostics specialist is an all-rounder and can go where needed, then three enlisted engineers to see to whatever needs fixing. I then gave the department a petty officer responsible for monitoring and maintaining environmental systems (located on another deck) with a crewman to assist (due to the importance of the system for the crews survival). Then added a petty officer in the impulse control room, again with a crewman to assist, due to the power of the Albacore's impulse drive, and its importance when on missions.