You can use the Username Availability script on your website by using the simply to use API.
The API is disabled on the demo
Simply point your website to the API url and parse the output.
API url: http://www.remotetweet.com/scripts/username/check.php?username=USERNAME
The script will output the following:
'available' - The username entered is available.
'unavailable' - The username entered is unavailable.
'suspended' - The username entered is suspended.
'invalid' - The username entered is invalid (Only A-Z, 0-9 and _ are valid characters).
'twitter' - The username entered includes the word twitter, which is forbidden.
'empty' - No username was entered.