You can perform an IP check when they access any part of your website.
In your admin panel you store a list of banned IP addresses in a database right ? So heres a solution with that in mind.
checkBannedIP();
function checkBannedIP() {
$ipAddresses = getBannnedIPs(); // Array('44.55.66.898', '465.22.78.365');
if(in_array($_SERVER['REMOTE_ADDR'], $ipAdresses)) {
header("Location: www.google.com");
}
}
All you need to do is created getBannedIPs() function which is a list of the IP's in your database.
So just have that function in a shared .php file and call checkBannedIP() at the top of every page on your site. This means it will redirect banned users IP to google.com. People messing about on sites are more likely to stop if they're frustrated with redirection.