Mrthdrb

If the English sentence were

It was a time of happiness, peace and joy.

would the German be the following?

Es war eine Zeit des Glücks, des Friedens und der Freude

That seems clumsy to me, but I also don't think a construction like

eine Zeit des Glücks, Friedens und (der?) Freude

is permissible.

Yes, you can omit repeated articles in genitive.

Wir gedenken der Verwundeten, Gefallenen und Vermissten des Krieges

Es war eine Zeit des Glücks, Friedens und fröhlichen Zusammenseins

The genitive is, while still present, one of the rarer cases in German.

So, while you can omit repeated articles in lists, you might want to refrain from doing so to clearly mark the genitive. Note I changed your example - mixed articles (omitted/present) in lists in genitive sound, while grammatically entirely correct, a bit awkward to a native speaker. So I would rather use your example as

Es war eine Zeit des Glücks, des Friedens und der Freude

instead of

Es war eine Zeit des Glücks, Friedens und der Freude

But that detail is more a matter of style than of grammar.

As an addition to tofro's answer I only want to point out/ stress some hints from the comments:

If you want to omit repeated articles than you often (not always*) need the first and (always) omit the rest.

You just have to be aware which nouns are part of your list to have omitted articles.

In comparison the two examples:

Wir gedenken der Verwundeten, der Gefallenen und der Vermissten des Krieges.=>

Wir gedenken der Verwundeten, Gefallenen und Vermissten des Krieges.

Es war eine Zeit des Glücks, des Friedens und des fröhlichen Zusammenseins.=>

Es war eine Zeit des Glücks, Friedens und fröhlichen Zusammenseins.

As you might see: des Kriegesis in genitive but not part of the list.

*As vectory points out, you can even have sentence constructions to omit all articles:

Eine Zeit voll Glück und Frieden. Im Gedenken an Verletzte, Gefallene und Vermisste des Krieges.

When to omit and when not?
In my opinion it depends on overall context. With the articles I can stress more the nouns, without it is more a "long concatenated list".

That is why I would prefer an die Verletzten, ... because it is feels like a reverent moment speaking about it. In other cases they make the sentence longer and I guess in speaking I would more likely omit them while in writing put the articles there. _{Or maybe just thinking about the sentence let me put them in and not long thinking omits them. Good question.}