separate categories with comma and srounded by single quote

Question

Welcome to WPSE faq! This type of question is probably best suited for suited for stackoverflow, rather than here as the question isn’t specifically related to WordPress. You just need to get an array of the IDs (a simple foreach loop could do this – or use the WordPress’ wp_list_pluck) and then explode that array:

//$categories is the array of category objects
$cat_ids = wp_list_pluck($categories,'term_id');
echo "'".implode(',',$cat_ids)."'";

Edit

And to incorporate this method into the OP’s code example:

<?php
$args=array(
'child_of' => 79
);
$categories=get_categories($args);
foreach($categories as $category) { 
    $cat_ids[] = $category->term_id;
}
echo "'".implode(',',$cat_ids)."'";
?>