The Mood Lantern Rings aren't based on emotions. They're based on sins.
The sins, in their classical expression,
lust (replaced luxuria (wasteful extravagance) )
acedia (acedia/discouragement -- became Sloth in modern versions)
We have the rings:
green (courage, allegedly) -- the sin, pride
yellow (fear) -- the sin is most likely gluttony. They feed on other people.
blue (hope) then becomes Envy, which kind of fits because they only work by being around green rings, as if they were envious of their power.
orange (greed) -- this is easy, greed.
red (anger) -- Also easy, wrath
purple (love/lust) -- Lust, of course
violet (compassion) -- given the degree to which they didn't do a damn thing when they had the chance to, "sloth" is the obvious answer.
The black and white rings don't fall into this category, but then, I had to shoehorn things a bit too.