Show Category Children But Hide "No Category" with Children List

Not sure I understand what you’re looking for here, but this would allow you to define what is displayed instead of “No Categories”:

$cat_id  = get_query_var( 'cat' );
$catlist = get_categories( 'child_of=' . $cat_id );
$no_cats = 'This is what will show instead of No Categories';

$args = array(
    'echo'             => 0,
    'orderby'          => 'id',
    'title_li'         => '',
    'child_of'         => $cat_id,
    'show_option_none' => $no_cats,
);
wp_list_categories( $args );

Just make $no_cats a string that contains whatever message or markup you want to show.

Thanks Shaun,
(I really appreciate your time)
Your code will actually answer what I originally wanted to do, which was just hide “No Categories” altogether or echo some other text.

I was trying to incorporate show_option_none and couldn’t figure it out.

I like the way you have written out the $arg = array(
It’s not shortcode and it helps me to understand php better. (which I really want to learn…)

Thanks again and I am marking this resolved!

p.s. In my first post I was trying to just re-display the children of the parent category instead of printing “No Categories”.

Here is the code (thanks Shaun) that worked for any future searchers.
Instead of changing the “No Categories” I elected to put a “Previous Page” link. I wrapped it in a div class so I could style it.
All I changed to Shaun’s code above is change the echo 0 to echo 1.

<div class="categorychildren">
<?php
$cat_id  = get_query_var( 'cat' );
$catlist = get_categories( 'child_of=' . $cat_id );
$no_cats = '<A HREF="javascript:javascript:history.go(-1)">Previous Page</A>';

$args = array(
    'echo'             => 1,
    'orderby'          => 'id',
    'title_li'         => '',
    'child_of'         => $cat_id,
    'show_option_none' => $no_cats,
);
wp_list_categories( $args );
?>
</div>

Awesome, glad I could help!