Domai.nr is a free service that suggests you short domain names corresponding to your domain. You can use those short domain names as URL shortening service, or can use with a service like Dlvr.it. It automatically finds valid extensions, and then give you suggestions.
Here are the suggestions that it gave for my domain name (the Text in Blue are the suggested domain names):
Domai.nr is quite simple to use. Just go to the website, and enter your domain name, and it will immediately give short domain suggestions. To register a domain, you can just click on name of that, and Domai.nr will show you the domain name registrars with whom you can register that domain name.
One shortcoming I found in Domai.nr is that it does not checks for availability of domain name while giving suggestions. But it does tells you about that when you click on the domain name.
Check out Domai.nr