to change the colour of the violin plot you use fill = variable, like this:
ggplot(diamonds, aes(x=cut,y=carat)) + geom_violin(aes(fill=cut))
same goes for boxplot
ggplot(diamonds, aes(x=cut,y=carat)) + geom_boxplot(aes(fill=cut))

but whatever value you have has to have the same value for each cut, that is, if you wanted to use for example mean depth/cut as the color variable you would have to code it.
with dplyr group your diamonds by cut and with summarize get the mean depth (or any other variable)
library(dplyr)
diamonds_group <- group_by(diamonds, cut)
diamonds_group <- summarize(diamonds_group, Mean_Price = mean(price))
Then I used diamonds2 as a copy of diamonds to then manipulate the dataset
diamonds2 <- diamonds
I merge both dataframes to get the Mean_Depth as a variable in diamonds2
diamonds2 <- merge(diamonds2, diamonds_group)
And now I can plot it with mean depth as a color variable
ggplot(diamonds2, aes(x=cut,y=carat)) + geom_boxplot(aes(fill=Mean_Price)) + scale_fill_gradient2(midpoint = mean(diamonds2$price))
