I love the name [name]Etta[/name], so any name that ends in “et”, such as [name]Violet[/name], I would probably give the nickname [name]Etta[/name].
I really like [name]Lettie[/name] and it’s the nickname I have paired with [name]Violet[/name].
[name]Lettie[/name] is cute.
Another suggestion is [name]Via[/name] or Vio
[name]Vi[/name] sounds like a heavy smoking truck stop waitress to me. I like Vio or [name]Lettie[/name]. There’s a show called Fresh Meat (on Hulu via BBC) with a character named [name]Violet[/name], called Vaude (rhymes with [name]Maude[/name]).
I like “purple” too, for a silly funny nickname (my DD’s silly nicknames range from “MOMO” to peanut butter). But for a name that you would call your child every day I like [name]Lettie[/name] better than [name]Vi[/name] and I like [name]Vivi[/name] best of all!
I always liked Veeve for [name]Violet[/name], also [name]Olly[/name] would make a more surprising choice 
I love [name]Lettie[/name] or even go shorter with [name]Ettie[/name]. so cute!
I don’t love [name]Lettie[/name] or [name]Vi[/name]…I actually think Purple is fun and unique!
I like vi and [name]Vivi[/name]. [name]Lettie[/name] is cute on paper, but when I say it out loud, I don’t like it as much. Same with ettie and [name]Etta[/name]. I think violet is lovely on its own and doesn’t need a nn, but my favorite nickname is vi.