If you have a website you could also host a file or redirect on that which client reads and your server updates.
So if your IP changes it updates mydomain.com/server.ip
Then the client reads mydomain.com/server.ip and use the provided ip to connect.
Another option is to use a HTTP/1.0 status code
write for example a PHP script that does:
PHP Code:
<?php
// Many pre-HTTP/1.1 user agents do not understand the 303 so we use 302
header('HTTP/1.0 302 Found');
header('Location: 123.45.67.89:8888');
Ofcourse the client should understand the 302 and react on that.