Take a look at the Tableau JavaScript API. Once you have your workbooks hosted with Tableau Online you can display them using the API on your own website. Then just share the link to those you want to have viewing rights.
This will be public to whoever has the link though unless you set the location up to require login.
http://onlinehelp.tableau.com/current/pro/online/windows/en-us/publish_workbooks_howto.html
http://onlinehelp.tableau.com/current/pro/online/windows/en-us/Img/publish9.png
When you see this window, click on a User/group, and click Edit. Tableau has default roles (Viewer, Interactor, etc.). You can modify the Interactor role so that it becomes a Custom role so that someone can't download your workbook, etc.
http://onlinehelp.tableau.com/current/pro/online/mac/en-us/publish_workbooks_permissions_add.html
See here for more details on permissions.