A good DB series or a good DB animation? Those are two different things.
Animation (as in something short akin to an OAV/movie) is easier to point at:
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Toyble's last chapter*
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Dragon Ball Elsewhere
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Yardrats, l'histoire d'un survivant
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Tsufurs
In short: those stories that fill a gap in the narrative and/or focus on other characters then the principal cast.
Also quite nice could be
Who wants to be a Superhero ? and
Wrong Time** but I'd prefer something that adds to the story and is not just "I master DB storytelling and want to have fun with it". The franchise gives us that already and I prefer my media info-packed. But that's just me.
As to a longer animation - so a series - I can't really see anything fan-created as worthy of getting animated and canonized. Basically there are three types of fan works: an alternative universe (and I'm not interested in those at all, I love coherence [I know DB isn't really a coherent world, but I don't want to rob it of the precious few that's left] but there are some good titles there: DBSF, Universe F, Ankoku, Dragon Ball Sai, DBM's various special chapters and a special mention here for Dragon ball Dimensions - the great branching, comprehensive what-if of the Buu Saga), a DB-derivative, non-imaginative AF (DBNA, DBEX are some of the worst offenders with youngjiji's DBAfter coming in a close second and both toyble's and youngjiji's respective AFs doing a surprisingly not bad work of being readable) and then there's DBM the tournament (I have discussed the special chapters in the "alternative universes" section so here I'm referring just to the main story).
I love DBM (as is easily attested by the fact that I translate it into Polish since 2008) but I wouldn't want it to become official. The idea of DBM is to show fun fights, interesting what-if encounters - in short to be pure entertainment. Sure, there's an overarching plot, even quite an engrossing one, but I'm not sure I'd want the Dragon Ball franchise to come back for yet another tournament arc. Enough's enough, we've had many of those already. What's good for a very slow fan endeavour, isn't guaranteed to be the same for a professional series. So no, I don't consider animating DBM a good idea.
So, what's left? Nothing. It would seem that, were I to decide, I'd surely use some fan works as a basis for new DB material, but I wouldn't create any new series, just more feature films.
One more thing: GT:Revised. It is probably the perfect DB fanfiction but I'm not sure its changes are so huge as to warrant a whole new series - rather a Kai-like reworking of GT with some new scenes added/redone. So I don't count it as pertinent to this topic.
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* That's the only fan thing I'd really love to see turned official. It's spot-on Dragon Ball and I dare you to read without shedding a tear. That's how GT should have ended. It's such a perfect closure to the Dragon World.
** BTW, I don't consider Wrong Time an alternative history - I can see it as fitting into the the standard timeline.
. Aladjinn Arc in New Age would make a good what if OVA. But personally I'll go with Legacy of Son Gohan 
. Story about Grandpa Gohan 
. I hardly see him in fanfiction and he isn't even mentioned in DBMV. No other fan manga mentions him either. So it's nice to see Goku's gramps have a central role. Nice seeing him fight Oozaru too.
