function get_coupons_from_email( $current_email  ) {
    global $wpdb;

    return $wpdb->get_col( $wpdb->prepare("
        SELECT p.post_name
        FROM {$wpdb->prefix}posts p
        INNER JOIN {$wpdb->prefix}postmeta pm
            ON p.ID = pm.post_id
        WHERE p.post_type = 'shop_coupon'
            AND pm.meta_key = 'customer_email'
            AND pm.meta_value LIKE '%s'
        ORDER BY p.post_name DESC
    ", '%'.$current_email.'%' ) );
}

After some self reading, I manage to find the answer I need. 
The meta value for LIKE must use the symbol '% value %' which I don't know earlier. I have mistakenly deleted the symbol %.