Sadly, you have missed the golden age, the era of the "glowing magenta giant" - a kind of gas giant that appeared bright, hot magenta. They were about as rare as glowing green giants. However, while glowing green giants were deemed harmless (and even canonized as a proper variant of gas giants), magenta giants caused instability bugs, and so were patched away. All we have left are
the memories.
These kind of mauve-coloured or perhaps lilac-coloured gas giants (almost always a variant of Class III colouration) are the best we can offer in terms of pinkness these days.
As for rarity, they are perhaps more common than you might think. They are sufficiently common that they aren't usually posted on the forums whenever someone spots one. Maybe about one in a thousand Class III giants would qualify as "pink"? That still leaves billions of 'em scattered about the place.