One color to category link depending on category ID

Open the page which is rendering the category posts, and in the appropriate place (before running the loop) write the following code

<?php
$catid = get_cat_id();
$color = "#222"; //default;
if ($catid == $pinkCategoryId) $color = "#8B0A50";
else if ($catid == $redCategoryId) $color = "#FF0000";
?>

<style type="text/css">
a { color: <?php echo $color;?>; }
</style>

Now adjust the code block above according to your need

You can also use it by category name instead of category id, just change the get_cat_id to get_the_category() which will return the current category name. Then you can perform the rest of the task as is