Neck attachment/tension problems - the solution depends on how the neck is attached. If it is not firm enough, you don't stand a chance of tuning without fixing the problem.
I don't know much about truss rods as I amused to older style banjoes with a perch pole extending as part of the neck.
There have been threads about repairing and adjusting banjoes which link to web sites dedicated to such problems. I'm not sure if the auto-links at the top of the page include the ones I recall, but try clicking on them as a starting point.
If no luck try a Forum Search - (Lyrics & Knowledge Search) - box at top of main forum page.
Quack!
Geoff the Duck.