How serious or light-hearted do you want the eulogy to be? A good eulogy need not be uniformly sombre, just appropriate. Some eulogy-writers take a serious approach, others are bold enough to add humour. Used cautiously, humour can help convey the personality of the deceased and illustrate some of his or her endearing qualities.
The tone can also be partially determined by the way the deceased passed away. If you’re giving a eulogy about a teenager who met an untimely death, then your tone would be more serious than it would if you were giving a eulogy about a grandparent who happily lived to see his ninetieth birthday.