What emotions can/can't be influenced in Harry Potter?

Question

In Harry Potter many emotions can be created by spells or potions. For example Ron is given a love potion which causes him to become infatuated with one of the girls in his year. Given that love (one of the most complex emotions) can be faked although not fully created by potions are there any examples of other emotions being influenced by magic or any canon examples of emotions that can't be influenced by magic. I would prefer quotes from the books but will accept Pottermore if there is nothing else.

Answer 1

There are many ways that magic can alter someone's emotional state in Harry Potter.

Cheering Charms

These put the target in a good humor. As indicated in Harry Potter and the Prisoner of Azkaban:

But Hermione didn't turn up all lesson.

"She could've done with a Cheering Charm on her too," said Ron as the class left for lunch, all grinning broadly -- the Cheering Charms had left them with a feeling of great contentment.

Hermione wasn't at lunch either. By the time they had finished their apple pie, the after-effects of the Cheering Charms were wearing off, and Harry and Ron had started to get slightly worried.

—Harry Potter and the Prisoner of Azkaban

Specifically, the Cheering Charm appears to make one content.

Love Potions

These potions do not produce love, but produce severe emotional alterations by inducing a strong obsession with the one who employs the potion.

Amortentia is the strongest love potion known to the magical community, and even it only produces an imitation. According to Slughorn in Half-Blood Prince:

“Amortentia doesn’t really create love, of course. It is impossible to manufacture or imitate love. No, this will simply cause a powerful infatuation or obsession.

—Harry Potter and the Half-Blood Prince

However, when Ron Weasley accidentally ingested a Love Potion created by Romilda Vane, he certainly exhibited a highly altered emotional state:

“I can’t stop thinking about her!” said Ron hoarsely. Harry gaped at him. He had not expected this and was not sure he wanted to hear it. Friends they might be, but if Ron started calling Lavender “Lav-Lav,” he would have to put his foot down.

“Why does that stop you having breakfast?” Harry asked, trying to inject a note of common sense into the proceedings.

“I don’t think she knows I exist,” said Ron with a desperate gesture.

“She definitely knows you exist,” said Harry, bewildered. “She keeps snogging you, doesn’t she?”

Ron blinked. “Who are you talking about?”

“Who are you talking about?” said Harry, with an increasing sense that all reason had dropped out of the conversation.

“Romilda Vane,” said Ron softly, and his whole face seemed to illuminate as he said it, as though hit by a ray of purest sunlight.

—Harry Potter and the Half-Blood Prince

Pogrebin

The Pogrebin appears to be able to induce feelings of extreme sadness in its victims, in order to subdue and consume them.

The Pogrebin is attracted to Humans, and enjoys trailing them. When the Human turns around, the Pogrebin crouches down, and, because of its large head, resembles a rock. If the creature manages to tail a Human for a few hours, a sense of despair and futility will wash over the Human. When the victim sits or sinks to its knees to weep, the Pogrebin attacks and attempts to devour them.

—Fantastic Beasts and Where to Find Them

Dementors

Dementors can cause feelings of despair or hopelessness in humans.

"I felt weird," said Ron, shifting his shoulders uncomfortably. "Like I'd never be cheerful again...."

—Harry Potter and the Prisoner of Azkaban

Or even fear:

Where there should have been eyes, there was only thin, gray scabbed skin, stretched blankly over empty sockets. But there was a mouth... a gaping, shapeless hole, sucking the air with the sound of a death rattle.

A paralyzing terror filled Harry so that he couldn't move or speak. His Patronus flickered and died.

—Harry Potter and the Prisoner of Azkaban

Harry's link with Voldemort

This can transmit whatever emotion Voldemort is feeling to Harry. For example, happiness:

Maniacal laughter was ringing in his ears... he was happier than he had been in a very long time... jubilant, ecstatic, triumphant... a wonderful, wonderful thing had happened...

—Harry Potter and the Order of the Phoenix

Or hatred:

At once, Harry's scar burned white-hot, as though the old wound had burst open again - and unbidden, unwanted, but terrifyingly strong, there rose within Harry a hatred so powerful he felt, for that instant, he would like nothing better than to strike - to bite - to sink his fangs into the man before him —

—Harry Potter and the Order of the Phoenix

Phoenix song

Phoenix song is magical; it is reputed to increase the courage of the pure of heart and to strike fear into the hearts of the impure.

—Fantastic Beasts and Where to Find Them

Indeed, it does have this effect:

Music was coming from somewhere. Riddle whirled around to stare down the empty Chamber. The music was growing louder. It was eerie, spine-tingling, unearthly; it lifted the hair on Harry’s scalp and made his heart feel as though it was swelling to twice its normal size. Then, as the music reached such a pitch that Harry felt it vibrating inside his own ribs, flames erupted at the top of the nearest pillar.

—Harry Potter and the Chamber of Secrets

These are a variety of mechanisms, but they seem to illustrate that there aren't many emotions that magic can't affect.

Answer 2

At least one plausible answer is love if you allow that love is an emotion.

Keeping in mind a couple of choice quotes from Dumbledore and Voldemort:

"You are protected, in short, by your ability to love! The only protection that can possibly work against the lure of power like Voldemort's! In spite of all the temptation you have endured, all the suffering, you remain pure of heart, as pure as you were five years ago, when you looked into a mirror that reflected your heart's desire. —Dumbledore

"The Boy Who Lived. How lies have fed your legend Harry. Shall I reveal what really happened that night thirteen years ago? Shall I divulge how I truly lost my powers? Yes, shall I? It was love. You see, when dear sweet Lily Potter gave her life for her only son... she provided the ultimate protection. I could not touch him. It was old magic. Something I should have foreseen. —Voldemort

Both of these indicate that Love is many leagues more powerful than even the strongest spells known, up to and including the forbidden curses. Chances are good you can't get away with influencing it with spells or potions. And, as Jonah pointed out, love potions don't actually force love onto somebody, just infatuation. The love that Dumbledore and Voldemort are talking about is beyond what the so-called love potion can influence.