Quick, get a copy of How to Talk So Kids Will Listen, and Listen So Kids Will Talk, by Faber and Mazlish. The wisdom in this book will make it a resource you reach for again and again. It's my current favorite with my 4.5yo grandson. The techniques and ideas are mutually respectful, and they work.
I've recommended this book to several families with young kids, including a couple who were as emotional as yours, and they started getting results as soon as they started applying the steps suggested in each chapter.
The primary technique that calms my grandson when he's getting worked up over something he can't have is to empathize with him sincerely. As in "I hear that you really, really want another story tonight. I love stories too, and if your sleep wasn't so important, I'd read with you all night. Wouldn't that be fun? It's time for you to sleep now, and I need to get some work done so I can sleep, too. Tomorrow, let's talk about getting to bed earlier so we'll have time for three stories. Would you like that?"
Once a child knows you have taken his desires seriously before ruling them out, his sense of fairness has often been met, and he's able to change the channel and do something else. This is often a bit more challenging at the end of the day when tiredness is part of the equation, so sometimes a meltdown occurs anyway. But if his emotional needs have been addressed, the emotions are generally less intense.
For some immediate information on this, google Emotion Coaching and read why empathetic parenting is so effective. We're not talking about pushover parenting. This is authoritative but kind coaching, working with the reality of the child's feelings and needs.