Open D tuning
Open D tuning is 5th = F# or A, 4th = D (same as G tuning), 3rd = F#, 2nd = A, 1st = D (same as G tuning)
Don't know of too many instances where this tuning is used. I believe Ralph Stanley uses it some. Any tuning is useful for various purposes, but many of the odd tunings present new fingering problems while they solve others. The central question on a tuning is does it facilitate picking out the melody, while keeping the desired chord tones. D tuning doesn't contribute a lot in this category.
Sugestion: try mountain modal tuning, but using G tuning and tuning the 2nd string up a half tone to C. You then have no chord on the open strings, but it rings this haunting hollow sound that just begs tinkering with unusual tunes on the strings; very Southern Appachian. In my opinion, one of most fun tunings created.
No suggestions, but Pete Seeger illustrates some bluesy sounds he developed for using the banjo on certail blues songs. I don't know if other players have perfected the banjo as a blues instrument, but it's a possibility. Basically try playing some blues riffs similar to guitar blues riffs. On the banjo, blues sound will be heavily single string playing along with slamming a few accenting chords. I would tend to use it only as a lead tune instrument for blues as basic chords don't really promote it as an accompanying chording instrument. Get a guitarist to back you for the harmony.
I'd be interested in hearing what are doing with blues on a banjo.