Take your pick:
"To say that we were happy doesn't even begin to say it."
"There are no words to describe how happy we were."
"Saying that we were happy would be a huge understatement."
"To say that we were happy is like saying that the surface of the Sun is unpleasantly warm*."
I don't think that a more literal and direct translation would properly express the meaning of the Russian. But perhaps my first example above ("...doesn't even begin to say it") is the most similar to "ничего не сказать".
* Or, "...like saying that Bill Gates is financially comfortable", or "...like saying that Osama bin Laden had a tendency to over-criticize Americans and Jews", etc.