If you process your cube daily, you could put a view on your time dimension.

The view simply adds a column that calculates for every day the relative position towards today.

For example, the column will read 'Today' for today's date (2013-03-20) and 'Yesterday' for 2013-03-19.

The next day, the column will display 'Yesterday' for 2013-03-20 and 'D - 2' for 2013-03-19 and so on.

This is very easy to implement in SQL.