A nickname describing a person who is so happy-go-lucky and excitable that you can almost see sunshine radiating from his or her perpetually smiling face. Generally, these people have huge mouths -- hence the dinosaur reference. People who see sunshineasauruses cannot help but be happy and smile along with them.
"wow, that's the biggest smile I've seen for a long time. Hey, I'm feeling kind of good... she must be a sunshineasaurus!"