I honestly don't think the Vacktor's have just one set emotion. Though they may feel one emotion more than the others they have expressed other emotions. 

Yellow

Fear of lightning

Fear of Purple

Fear of his new electrical powers

Fear of hurting the village

Sadness when he accidentally killed Pikachu and the chicken egg

Annoyed at Zeus minions, and Barney when he did not listening to him

Yellow was upset with losing

Upset with Rudolph having blue eyes because that's not canon

Green

In Spooky Tales he was freaked out about the werewolf coming and when Barney set the barn on fire

Yellow said he was smiling once

He was excited about luring the werewolf into a trap

Pink

Mentioned that she's cried before

She's also felt she was a failure before

Blue

Was angry at Nick for stealing his apple

He felt happiness when he scored a goal in soccer

He felt happiness at the bringing of Mean Tweets when he happily waved at the audience

Also Red said he was rude to him when he asked if he wanted to play hide n seek

 I wonder if when Yellow said bye to Barney in the Hunger Games when Barney was falling if he was actually saying bye because he was shutting down or something. It's most likely that he was saying goodbye as Barney fell to the void, but still... It makes me wonder

I wonder if when Yellow is talking how great he is, and talking about how cool and awesome he is if he's actually trying to convince himself that or something. Yellow tries to make friends with flowers and with animals. And though he says he has lots of friends it almost makes me wonder if he's actually talking about the animals and the flowers. Yellow only really a hangs out with Barney and his family so it makes me wonder if he has trouble making friends. I mean he does talk about weird stuff so it would make sense if he doesn't.