I am trying to create a contact list which is automatically generated from the users in a SharePoint Permissions Group within SharePoint 2010. Is this possible?
yes it is, look at this Post
Just got what you wanted to do
If the idea is to just use that list as a web part, then i suggest you to look at Site Users web part and add the web part to the landing page, this web part allows you to configure the SharePoint groups that you want it to be shown. The functionality of this web part is to list down all the members and also provide presence information using which you can send email, instant message and also get to see the information about the users from exchange server.